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Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology / / by Neculai Andrei
Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology / / by Neculai Andrei
Autore Andrei Neculai
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (XXIV, 506 p. 68 illus., 66 illus. in color.)
Disciplina 519.3
Collana Springer Optimization and Its Applications
Soggetto topico Mathematical optimization
Mathematical models
Algorithms
Optimization
Mathematical Modeling and Industrial Mathematics
ISBN 3-319-58356-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 2. Mathematical modeling using algebraically oriented languages for nonlinear optimization -- 3. Introduction to GAMS technology -- 4. Applications of continuous nonlinear optimization -- 5. Optimality conditions for continuous nonlinear optimization -- 6. Simple bound constraint optimization -- 7. Penalty and augmented Langrangian methods -- 8. Penalty-Barrier Algorithm -- 9. Linearly Constrained Augmented Lagrangian -- 10. Quadratic programming -- 11. Sequential quadratic programming -- 12. A SQP Method using only Equalit Constrained Sub-problem -- 12. A Sequential Quadratic Programming Algorithm with Successive Error Restoration -- 14. Active-set Sequential Linear-Quadratic Programming -- 15. A SQP algorithm for Large-Scale Constrained Optimization -- 16. Generalized Reduced Gradient with sequential linearization -- 17. Interior point methods -- 18. Filter methods -- 19. Interior Point Sequential Linear-Quadratic Programming -- 20. Interior Point Filer Line-Search IPOPT -- 21. Numerical studies.
Record Nr. UNINA-9910254296603321
Andrei Neculai  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
A derivative-free two level random search method for unconstrained optimization / / Neculai Andrei
A derivative-free two level random search method for unconstrained optimization / / Neculai Andrei
Autore Andrei Neculai
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (126 pages) : illustrations
Disciplina 519.6
Collana SpringerBriefs in Optimization
Soggetto topico Mathematical optimization
Optimització matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-68517-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466399303316
Andrei Neculai  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
A derivative-free two level random search method for unconstrained optimization / / Neculai Andrei
A derivative-free two level random search method for unconstrained optimization / / Neculai Andrei
Autore Andrei Neculai
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (126 pages) : illustrations
Disciplina 519.6
Collana SpringerBriefs in Optimization
Soggetto topico Mathematical optimization
Optimització matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-68517-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910484845603321
Andrei Neculai  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Modern numerical nonlinear optimization / / Neculai Andrei
Modern numerical nonlinear optimization / / Neculai Andrei
Autore Andrei Neculai
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (824 pages)
Disciplina 016.5192
Collana Springer Optimization and Its Applications
Soggetto topico Mathematical optimization
Algebras, Linear
Optimització matemàtica
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 9783031087202
9783031087196
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- List of Algorithms -- List of Applications -- List of Figures -- List of Tables -- 1: Introduction -- 1.1 Mathematical Modeling: Linguistic Models Versus Mathematical Models -- 1.2 Mathematical Modeling and Computational Sciences -- 1.3 The Modern Modeling Scheme for Optimization -- 1.4 Classification of Optimization Problems -- 1.5 Optimization Algorithms -- 1.6 Collections of Applications for Numerical Experiments -- 1.7 Comparison of Algorithms -- 1.8 The Structure of the Book -- 2: Fundamentals on Unconstrained Optimization. Stepsize Computation -- 2.1 The Problem -- 2.2 Fundamentals on the Convergence of the Line-Search Methods -- 2.3 The General Algorithm for Unconstrained Optimization -- 2.4 Convergence of the Algorithm with Exact Line-Search -- 2.5 Inexact Line-Search Methods -- 2.6 Convergence of the Algorithm with Inexact Line-Search -- 2.7 Three Fortran Implementations of the Inexact Line-Search -- 2.8 Numerical Studies: Stepsize Computation -- 3: Steepest Descent Methods -- 3.1 The Steepest Descent -- Convergence of the Steepest Descent Method for Quadratic Functions -- Inequality of Kantorovich -- Numerical Study -- Convergence of the Steepest Descent Method for General Functions -- 3.2 The Relaxed Steepest Descent -- Numerical Study: SDB Versus RSDB -- 3.3 The Accelerated Steepest Descent -- Numerical Study -- 3.4 Comments on the Acceleration Scheme -- 4: The Newton Method -- 4.1 The Newton Method for Solving Nonlinear Algebraic Systems -- 4.2 The Gauss-Newton Method -- 4.3 The Newton Method for Function Minimization -- 4.4 The Newton Method with Line-Search -- 4.5 Analysis of Complexity -- 4.6 The Modified Newton Method -- 4.7 The Newton Method with Finite-Differences -- 4.8 Errors in Functions, Gradients, and Hessians -- 4.9 Negative Curvature Direction Methods -- 4.10 The Composite Newton Method.
5: Conjugate Gradient Methods -- 5.1 The Concept of Nonlinear Conjugate Gradient -- 5.2 The Linear Conjugate Gradient Method -- The Linear Conjugate Gradient Algorithm -- Convergence Rate of the Linear Conjugate Gradient Algorithm -- Preconditioning -- Incomplete Cholesky Factorization -- Comparison of the Convergence Rate of the Linear Conjugate Gradient and of the Steepest Descent -- 5.3 General Convergence Results for Nonlinear Conjugate Gradient Methods -- Convergence Under the Strong Wolfe Line-Search -- Convergence Under the Wolfe Line-Search -- 5.4 Standard Conjugate Gradient Methods -- Conjugate Gradient Methods with gk+12 in the Numerator of βk -- The Fletcher-Reeves Method -- The CD Method -- The Dai-Yuan Method -- Conjugate Gradient Methods with in the Numerator of βk -- The Polak-Ribière-Polyak Method -- The Hestenes-Stiefel Method -- The Liu-Storey Method -- Numerical Study: Standard Conjugate Gradient Methods -- 5.5 Hybrid Conjugate Gradient Methods -- Hybrid Conjugate Gradient Methods Based on the Projection Concept -- Numerical Study: Hybrid Conjugate Gradient Methods -- Hybrid Conjugate Gradient Methods as Convex Combinations of the Standard Conjugate Gradient Methods -- The Hybrid Convex Combination of LS and DY -- Numerical Study: NDLSDY -- 5.6 Conjugate Gradient Methods as Modifications of the Standard Schemes -- The Dai-Liao Conjugate Gradient Method -- The Conjugate Gradient with Guaranteed Descent (CG-DESCENT) -- Numerical Study: CG-DESCENT -- The Conjugate Gradient with Guaranteed Descent and Conjugacy Conditions and a Modified Wolfe Line-Search (DESCON) -- Numerical Study: DESCON -- 5.7 Conjugate Gradient Methods Memoryless BFGS Preconditioned -- The Memoryless BFGS Preconditioned Conjugate Gradient (CONMIN) -- Numerical Study: CONMIN.
The Conjugate Gradient Method Closest to the Scaled Memoryless BFGS Search Direction (DK / CGOPT) -- Numerical Study: DK/CGOPT -- 5.8 Solving Large-Scale Applications -- 6: Quasi-Newton Methods -- 6.1 DFP and BFGS Methods -- 6.2 Modifications of the BFGS Method -- 6.3 Quasi-Newton Methods with Diagonal Updating of the Hessian -- 6.4 Limited-Memory Quasi-Newton Methods -- 6.5 The SR1 Method -- 6.6 Sparse Quasi-Newton Updates -- 6.7 Quasi-Newton Methods and Separable Functions -- 6.8 Solving Large-Scale Applications -- 7: Inexact Newton Methods -- 7.1 The Inexact Newton Method for Nonlinear Algebraic Systems -- 7.2 Inexact Newton Methods for Functions Minimization -- 7.3 The Line-Search Newton-CG Method -- 7.4 Comparison of TN Versus Conjugate Gradient Algorithms -- 7.5 Comparison of TN Versus L-BFGS -- 7.6 Solving Large-Scale Applications -- 8: The Trust-Region Method -- 8.1 The Trust-Region -- 8.2 Algorithms Based on the Cauchy Point -- 8.3 The Trust-Region Newton-CG Method -- 8.4 The Global Convergence -- 8.5 Iterative Solution of the Subproblem -- 8.6 The Scaled Trust-Region -- 9: Direct Methods for Unconstrained Optimization -- 9.1 The NELMED Algorithm -- 9.2 The NEWUOA Algorithm -- 9.3 The DEEPS Algorithm -- 9.4 Numerical Study: NELMED, NEWUOA, and DEEPS -- 10: Constrained Nonlinear Optimization Methods: An Overview -- 10.1 Convergence Tests -- 10.2 Infeasible Points -- 10.3 Approximate Subproblem: Local Models and Their Solving -- 10.4 Globalization Strategy: Convergence from Remote Starting Points -- 10.5 The Refining the Local Model -- 11: Optimality Conditions for Nonlinear Optimization -- 11.1 General Concepts in Nonlinear Optimization -- 11.2 Optimality Conditions for Unconstrained Optimization -- 11.3 Optimality Conditions for Problems with Inequality Constraints -- 11.4 Optimality Conditions for Problems with Equality Constraints.
11.5 Optimality Conditions for General Nonlinear Optimization Problems -- 11.6 Duality -- 12: Simple Bound Constrained Optimization -- 12.1 Necessary Conditions for Optimality -- 12.2 Sufficient Conditions for Optimality -- 12.3 Methods for Solving Simple Bound Optimization Problems -- 12.4 The Spectral Projected Gradient Method (SPG) -- Numerical Study-SPG: Quadratic Interpolation versus Cubic Interpolation -- 12.5 L-BFGS with Simple Bounds (L-BFGS-B) -- Numerical Study: L-BFGS-B Versus SPG -- 12.6 Truncated Newton with Simple Bounds (TNBC) -- 12.7 Applications -- Application A1 (Elastic-Plastic Torsion) -- Application A2 (Pressure Distribution in a Journal Bearing) -- Application A3 (Optimal Design with Composite Materials) -- Application A4 (Steady-State Combustion) -- Application A6 (Inhomogeneous Superconductors: 1-D Ginzburg-Landau) -- 13: Quadratic Programming -- 13.1 Equality Constrained Quadratic Programming -- Factorization of the Full KKT System -- The Schur-Complement Method -- The Null-Space Method -- Large-Scale Problems -- The Conjugate Gradient Applied to the Reduced System -- The Projected Conjugate Gradient Method -- 13.2 Inequality Constrained Quadratic Programming -- The Primal Active-Set Method -- An Algorithm for Positive Definite Hessian -- Reduced Gradient for Inequality Constraints -- The Reduced Gradient for Simple Bounds -- The Primal-Dual Active-Set Method -- 13.3 Interior Point Methods -- Stepsize Selection -- 13.4 Methods for Convex QP Problems with Equality Constraints -- 13.5 Quadratic Programming with Simple Bounds: The Gradient Projection Method -- The Cauchy Point -- Subproblem Minimization -- 13.6 Elimination of Variables -- 14: Penalty and Augmented Lagrangian Methods -- 14.1 The Quadratic Penalty Method -- 14.2 The Nonsmooth Penalty Method -- 14.3 The Augmented Lagrangian Method.
14.4 Criticism of the Penalty and Augmented Lagrangian Methods -- 14.5 A Penalty-Barrier Algorithm (SPENBAR) -- The Penalty-Barrier Method -- Global Convergence -- Numerical Study-SPENBAR: Solving Applications from the LACOP Collection -- 14.6 The Linearly Constrained Augmented Lagrangian (MINOS) -- MINOS for Linear Constraints -- Numerical Study: MINOS for Linear Programming -- MINOS for Nonlinear Constraints -- Numerical Study-MINOS: Solving Applications from the LACOP Collection -- 15: Sequential Quadratic Programming -- 15.1 A Simple Approach to SQP -- 15.2 Reduced-Hessian Quasi-Newton Approximations -- 15.3 Merit Functions -- 15.4 Second-Order Correction (Maratos Effect) -- 15.5 The Line-Search SQP Algorithm -- 15.6 The Trust-Region SQP Algorithm -- 15.7 Sequential Linear-Quadratic Programming (SLQP) -- 15.8 A SQP Algorithm for Large-Scale-Constrained Optimization (SNOPT) -- 15.9 A SQP Algorithm with Successive Error Restoration (NLPQLP) -- 15.10 Active-Set Sequential Linear-Quadratic Programming (KNITRO/ACTIVE) -- 16: Primal Methods: The Generalized Reduced Gradient with Sequential Linearization -- 16.1 Feasible Direction Methods -- 16.2 Active Set Methods -- 16.3 The Gradient Projection Method -- 16.4 The Reduced Gradient Method -- 16.5 The Convex Simplex Method -- 16.6 The Generalized Reduced Gradient Method (GRG) -- 16.7 GRG with Sequential Linear or Sequential Quadratic Programming (CONOPT) -- 17: Interior-Point Methods -- 17.1 Prototype of the Interior-Point Algorithm -- 17.2 Aspects of the Algorithmic Developments -- 17.3 Line-Search Interior-Point Algorithm -- 17.4 A Variant of the Line-Search Interior-Point Algorithm -- 17.5 Trust-Region Interior-Point Algorithm -- 17.6 Interior-Point Sequential Linear-Quadratic Programming (KNITRO/INTERIOR) -- 18: Filter Methods -- 18.1 Sequential Linear Programming Filter Algorithm.
18.2 Sequential Quadratic Programming Filter Algorithm.
Record Nr. UNINA-9910619281203321
Andrei Neculai  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Modern numerical nonlinear optimization / / Neculai Andrei
Modern numerical nonlinear optimization / / Neculai Andrei
Autore Andrei Neculai
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (824 pages)
Disciplina 016.5192
Collana Springer Optimization and Its Applications
Soggetto topico Mathematical optimization
Algebras, Linear
Optimització matemàtica
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 9783031087202
9783031087196
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- List of Algorithms -- List of Applications -- List of Figures -- List of Tables -- 1: Introduction -- 1.1 Mathematical Modeling: Linguistic Models Versus Mathematical Models -- 1.2 Mathematical Modeling and Computational Sciences -- 1.3 The Modern Modeling Scheme for Optimization -- 1.4 Classification of Optimization Problems -- 1.5 Optimization Algorithms -- 1.6 Collections of Applications for Numerical Experiments -- 1.7 Comparison of Algorithms -- 1.8 The Structure of the Book -- 2: Fundamentals on Unconstrained Optimization. Stepsize Computation -- 2.1 The Problem -- 2.2 Fundamentals on the Convergence of the Line-Search Methods -- 2.3 The General Algorithm for Unconstrained Optimization -- 2.4 Convergence of the Algorithm with Exact Line-Search -- 2.5 Inexact Line-Search Methods -- 2.6 Convergence of the Algorithm with Inexact Line-Search -- 2.7 Three Fortran Implementations of the Inexact Line-Search -- 2.8 Numerical Studies: Stepsize Computation -- 3: Steepest Descent Methods -- 3.1 The Steepest Descent -- Convergence of the Steepest Descent Method for Quadratic Functions -- Inequality of Kantorovich -- Numerical Study -- Convergence of the Steepest Descent Method for General Functions -- 3.2 The Relaxed Steepest Descent -- Numerical Study: SDB Versus RSDB -- 3.3 The Accelerated Steepest Descent -- Numerical Study -- 3.4 Comments on the Acceleration Scheme -- 4: The Newton Method -- 4.1 The Newton Method for Solving Nonlinear Algebraic Systems -- 4.2 The Gauss-Newton Method -- 4.3 The Newton Method for Function Minimization -- 4.4 The Newton Method with Line-Search -- 4.5 Analysis of Complexity -- 4.6 The Modified Newton Method -- 4.7 The Newton Method with Finite-Differences -- 4.8 Errors in Functions, Gradients, and Hessians -- 4.9 Negative Curvature Direction Methods -- 4.10 The Composite Newton Method.
5: Conjugate Gradient Methods -- 5.1 The Concept of Nonlinear Conjugate Gradient -- 5.2 The Linear Conjugate Gradient Method -- The Linear Conjugate Gradient Algorithm -- Convergence Rate of the Linear Conjugate Gradient Algorithm -- Preconditioning -- Incomplete Cholesky Factorization -- Comparison of the Convergence Rate of the Linear Conjugate Gradient and of the Steepest Descent -- 5.3 General Convergence Results for Nonlinear Conjugate Gradient Methods -- Convergence Under the Strong Wolfe Line-Search -- Convergence Under the Wolfe Line-Search -- 5.4 Standard Conjugate Gradient Methods -- Conjugate Gradient Methods with gk+12 in the Numerator of βk -- The Fletcher-Reeves Method -- The CD Method -- The Dai-Yuan Method -- Conjugate Gradient Methods with in the Numerator of βk -- The Polak-Ribière-Polyak Method -- The Hestenes-Stiefel Method -- The Liu-Storey Method -- Numerical Study: Standard Conjugate Gradient Methods -- 5.5 Hybrid Conjugate Gradient Methods -- Hybrid Conjugate Gradient Methods Based on the Projection Concept -- Numerical Study: Hybrid Conjugate Gradient Methods -- Hybrid Conjugate Gradient Methods as Convex Combinations of the Standard Conjugate Gradient Methods -- The Hybrid Convex Combination of LS and DY -- Numerical Study: NDLSDY -- 5.6 Conjugate Gradient Methods as Modifications of the Standard Schemes -- The Dai-Liao Conjugate Gradient Method -- The Conjugate Gradient with Guaranteed Descent (CG-DESCENT) -- Numerical Study: CG-DESCENT -- The Conjugate Gradient with Guaranteed Descent and Conjugacy Conditions and a Modified Wolfe Line-Search (DESCON) -- Numerical Study: DESCON -- 5.7 Conjugate Gradient Methods Memoryless BFGS Preconditioned -- The Memoryless BFGS Preconditioned Conjugate Gradient (CONMIN) -- Numerical Study: CONMIN.
The Conjugate Gradient Method Closest to the Scaled Memoryless BFGS Search Direction (DK / CGOPT) -- Numerical Study: DK/CGOPT -- 5.8 Solving Large-Scale Applications -- 6: Quasi-Newton Methods -- 6.1 DFP and BFGS Methods -- 6.2 Modifications of the BFGS Method -- 6.3 Quasi-Newton Methods with Diagonal Updating of the Hessian -- 6.4 Limited-Memory Quasi-Newton Methods -- 6.5 The SR1 Method -- 6.6 Sparse Quasi-Newton Updates -- 6.7 Quasi-Newton Methods and Separable Functions -- 6.8 Solving Large-Scale Applications -- 7: Inexact Newton Methods -- 7.1 The Inexact Newton Method for Nonlinear Algebraic Systems -- 7.2 Inexact Newton Methods for Functions Minimization -- 7.3 The Line-Search Newton-CG Method -- 7.4 Comparison of TN Versus Conjugate Gradient Algorithms -- 7.5 Comparison of TN Versus L-BFGS -- 7.6 Solving Large-Scale Applications -- 8: The Trust-Region Method -- 8.1 The Trust-Region -- 8.2 Algorithms Based on the Cauchy Point -- 8.3 The Trust-Region Newton-CG Method -- 8.4 The Global Convergence -- 8.5 Iterative Solution of the Subproblem -- 8.6 The Scaled Trust-Region -- 9: Direct Methods for Unconstrained Optimization -- 9.1 The NELMED Algorithm -- 9.2 The NEWUOA Algorithm -- 9.3 The DEEPS Algorithm -- 9.4 Numerical Study: NELMED, NEWUOA, and DEEPS -- 10: Constrained Nonlinear Optimization Methods: An Overview -- 10.1 Convergence Tests -- 10.2 Infeasible Points -- 10.3 Approximate Subproblem: Local Models and Their Solving -- 10.4 Globalization Strategy: Convergence from Remote Starting Points -- 10.5 The Refining the Local Model -- 11: Optimality Conditions for Nonlinear Optimization -- 11.1 General Concepts in Nonlinear Optimization -- 11.2 Optimality Conditions for Unconstrained Optimization -- 11.3 Optimality Conditions for Problems with Inequality Constraints -- 11.4 Optimality Conditions for Problems with Equality Constraints.
11.5 Optimality Conditions for General Nonlinear Optimization Problems -- 11.6 Duality -- 12: Simple Bound Constrained Optimization -- 12.1 Necessary Conditions for Optimality -- 12.2 Sufficient Conditions for Optimality -- 12.3 Methods for Solving Simple Bound Optimization Problems -- 12.4 The Spectral Projected Gradient Method (SPG) -- Numerical Study-SPG: Quadratic Interpolation versus Cubic Interpolation -- 12.5 L-BFGS with Simple Bounds (L-BFGS-B) -- Numerical Study: L-BFGS-B Versus SPG -- 12.6 Truncated Newton with Simple Bounds (TNBC) -- 12.7 Applications -- Application A1 (Elastic-Plastic Torsion) -- Application A2 (Pressure Distribution in a Journal Bearing) -- Application A3 (Optimal Design with Composite Materials) -- Application A4 (Steady-State Combustion) -- Application A6 (Inhomogeneous Superconductors: 1-D Ginzburg-Landau) -- 13: Quadratic Programming -- 13.1 Equality Constrained Quadratic Programming -- Factorization of the Full KKT System -- The Schur-Complement Method -- The Null-Space Method -- Large-Scale Problems -- The Conjugate Gradient Applied to the Reduced System -- The Projected Conjugate Gradient Method -- 13.2 Inequality Constrained Quadratic Programming -- The Primal Active-Set Method -- An Algorithm for Positive Definite Hessian -- Reduced Gradient for Inequality Constraints -- The Reduced Gradient for Simple Bounds -- The Primal-Dual Active-Set Method -- 13.3 Interior Point Methods -- Stepsize Selection -- 13.4 Methods for Convex QP Problems with Equality Constraints -- 13.5 Quadratic Programming with Simple Bounds: The Gradient Projection Method -- The Cauchy Point -- Subproblem Minimization -- 13.6 Elimination of Variables -- 14: Penalty and Augmented Lagrangian Methods -- 14.1 The Quadratic Penalty Method -- 14.2 The Nonsmooth Penalty Method -- 14.3 The Augmented Lagrangian Method.
14.4 Criticism of the Penalty and Augmented Lagrangian Methods -- 14.5 A Penalty-Barrier Algorithm (SPENBAR) -- The Penalty-Barrier Method -- Global Convergence -- Numerical Study-SPENBAR: Solving Applications from the LACOP Collection -- 14.6 The Linearly Constrained Augmented Lagrangian (MINOS) -- MINOS for Linear Constraints -- Numerical Study: MINOS for Linear Programming -- MINOS for Nonlinear Constraints -- Numerical Study-MINOS: Solving Applications from the LACOP Collection -- 15: Sequential Quadratic Programming -- 15.1 A Simple Approach to SQP -- 15.2 Reduced-Hessian Quasi-Newton Approximations -- 15.3 Merit Functions -- 15.4 Second-Order Correction (Maratos Effect) -- 15.5 The Line-Search SQP Algorithm -- 15.6 The Trust-Region SQP Algorithm -- 15.7 Sequential Linear-Quadratic Programming (SLQP) -- 15.8 A SQP Algorithm for Large-Scale-Constrained Optimization (SNOPT) -- 15.9 A SQP Algorithm with Successive Error Restoration (NLPQLP) -- 15.10 Active-Set Sequential Linear-Quadratic Programming (KNITRO/ACTIVE) -- 16: Primal Methods: The Generalized Reduced Gradient with Sequential Linearization -- 16.1 Feasible Direction Methods -- 16.2 Active Set Methods -- 16.3 The Gradient Projection Method -- 16.4 The Reduced Gradient Method -- 16.5 The Convex Simplex Method -- 16.6 The Generalized Reduced Gradient Method (GRG) -- 16.7 GRG with Sequential Linear or Sequential Quadratic Programming (CONOPT) -- 17: Interior-Point Methods -- 17.1 Prototype of the Interior-Point Algorithm -- 17.2 Aspects of the Algorithmic Developments -- 17.3 Line-Search Interior-Point Algorithm -- 17.4 A Variant of the Line-Search Interior-Point Algorithm -- 17.5 Trust-Region Interior-Point Algorithm -- 17.6 Interior-Point Sequential Linear-Quadratic Programming (KNITRO/INTERIOR) -- 18: Filter Methods -- 18.1 Sequential Linear Programming Filter Algorithm.
18.2 Sequential Quadratic Programming Filter Algorithm.
Record Nr. UNISA-996495169603316
Andrei Neculai  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Nonlinear Conjugate Gradient Methods for Unconstrained Optimization [[electronic resource] /] / by Neculai Andrei
Nonlinear Conjugate Gradient Methods for Unconstrained Optimization [[electronic resource] /] / by Neculai Andrei
Autore Andrei Neculai
Edizione [1st ed. 2020.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Descrizione fisica 1 online resource (515 pages)
Disciplina 512.5
Collana Springer Optimization and Its Applications
Soggetto topico Mathematical optimization
Mathematical models
Optimization
Mathematical Modeling and Industrial Mathematics
ISBN 3-030-42950-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 2. Linear Conjugate Gradient Algorithm -- 3. General Convergence Results for Nonlinear Conjugate Gradient Methods -- 4. Standard Conjugate Gradient Methods -- 5. Acceleration of Conjugate Gradient Algorithms -- 6. Hybrid and Parameterized Conjugate Gradient Methods -- 7. Conjugate Gradient Methods as Modifications of the Standard Schemes -- 8. Conjugate Gradient Methods Memoryless BFGS Preconditioned -- 9. Three-Term Conjugate Gradient Methods -- 10. Other Conjugate Gradient Methods -- 11. Discussion and Conclusions -- References -- Author Index -- Subject Index.
Record Nr. UNISA-996418199103316
Andrei Neculai  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Nonlinear Conjugate Gradient Methods for Unconstrained Optimization / / by Neculai Andrei
Nonlinear Conjugate Gradient Methods for Unconstrained Optimization / / by Neculai Andrei
Autore Andrei Neculai
Edizione [1st ed. 2020.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Descrizione fisica 1 online resource (515 pages)
Disciplina 512.5
512.94
Collana Springer Optimization and Its Applications
Soggetto topico Mathematical optimization
Mathematical models
Optimization
Mathematical Modeling and Industrial Mathematics
ISBN 3-030-42950-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 2. Linear Conjugate Gradient Algorithm -- 3. General Convergence Results for Nonlinear Conjugate Gradient Methods -- 4. Standard Conjugate Gradient Methods -- 5. Acceleration of Conjugate Gradient Algorithms -- 6. Hybrid and Parameterized Conjugate Gradient Methods -- 7. Conjugate Gradient Methods as Modifications of the Standard Schemes -- 8. Conjugate Gradient Methods Memoryless BFGS Preconditioned -- 9. Three-Term Conjugate Gradient Methods -- 10. Other Conjugate Gradient Methods -- 11. Discussion and Conclusions -- References -- Author Index -- Subject Index.
Record Nr. UNINA-9910484234603321
Andrei Neculai  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Nonlinear optimization applications using the GAMS technology / / Neculai Andrei
Nonlinear optimization applications using the GAMS technology / / Neculai Andrei
Autore Andrei Neculai
Edizione [1st ed. 2013.]
Pubbl/distr/stampa New York, : Springer, 2013
Descrizione fisica 1 online resource (xxii, 340 pages) : illustrations (some color)
Disciplina 003.75
Collana Springer optimization and its applications
Soggetto topico Nonlinear theories
Mathematical analysis
ISBN 1-4614-6797-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- List of Figures -- List of Applications -- 1. Mathematical Modeling Using Algebraic Oriented Languages -- 2. Introduction to GAMS Technology -- 3. Nonlinear Optimization Applications in GAMS Technology -- References -- Subject Index -- Author Index.
Record Nr. UNINA-9910739433203321
Andrei Neculai  
New York, : Springer, 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui