Numerical analysis and optimization : NAO-V, Muscat, Oman, January 2020 / / Mehiddin Al-Baali, Anton Purnama, Lucio Grandinetti, editors

• Record Nr.: UNINA9910512306803321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-72040-3
• Descrizione fisica: 1 online resource (307 pages)
• Collana: Springer proceedings in mathematics and statistics ; ; Volume 354
• Disciplina: 519.3
• Soggetti: Mathematical optimization; Numerical analysis; Anàlisi numèrica; Congressos; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- A Personal Perspective on Numerical Analysis and Optimization -- A Personal View of Numerical Analysis and Optimization -- Contents -- Contributors -- A New Inexact Nonmonotone Filter Sequential Quadratic Programming Algorithm -- 1 Introduction -- 2 Preliminaries -- 3 FiSQP Algorithm -- 4 iFiSQP Algorithm -- 5 Experimental Results -- 6 Concluding Remarks -- References -- Behavior of Limited Memory BFGS When Applied to Nonsmooth Functions and Their Nesterov Smoothings -- 1 Introduction -- 2 Limited Memory BFGS for Nonsmooth Optimization in Theory -- 2.1 Armijo-Wolfe Line Search -- 2.2 Full BFGS -- 2.3 Limited Memory BFGS -- 3 Limited Memory BFGS for Nonsmooth Optimization in Practice -- 3.1 Nesterov's Les Houches Problem -- 3.2 Smoothed Versions of Nesterov's Les Houches Problem -- 3.3 Max Eigenvalue Problem -- 3.4 Smoothed Max Eigenvalue Problem -- 3.5 Semidefinite Programming -- 3.6 Max Cut Problem -- 3.7 Smoothed Max Cut Problem -- 3.8 Matrix Completion Problem -- 3.9 Smoothed Matrix Completion Problem -- 4 Concluding Remarks -- References -- Subgradient Smoothing Method for Nonsmooth Nonconvex ; Optimization -- 1 Introduction -- 2 Preliminaries -- 3 Theoretical Background -- 4 Minimization Algorithm -- 4.1 Computation of Descent Directions -- 4.2 Solving Subproblem in Finding Search Directions -- 4.3 Minimization Algorithms -- 5 Numerical Experiments -- 6 Conclusions -- References -- On Some Optimization Problems that Can Be Solved in O(n) Time -- 1 Introduction -- 2 Preliminaries -- 2.1 Duality -- 2.2 Basic Lemmas -- 2.3 Simplifying Observations -- 2.4 Easy and Harder Cases -- 3 Analysis of the Nine Problems -- 3.1 Problems of Type (1,1) -- 3.2 Problems of Type (1,2) -- 3.3 Problems of Type (1,infty) -- 3.4 Problems of Type (2,1) -- 3.5 Problems of Type (2,2) -- 3.6 Problems of Type (2,infty).; 3.7 Problems of Type (infty,1) -- 3.8 Problems of Type (infty,2) -- 3.9 Problems of Type (infty,infty) -- 4 Concluding Remarks -- References -- Iteration Complexity of a Fixed-Stepsize SQP Method for Nonconvex Optimization with Convex Constraints -- 1 Introduction -- 2 Preliminaries -- 2.1 Stationarity and Constraint Qualifications -- 2.2 Giving an Explicit Bound on the Multipliers -- 2.3 Detecting Stationarity -- 3 Complexity Analysis -- 4 Conclusions -- References -- Modelling and Inferring the Triggering Function in a Self-Exciting Point Process -- 1 Introduction -- 2 Background -- 3 Non-parametric Estimation -- 4 Parametric Trigger Models -- 5 Parametrised Trigger on Real Data -- 5.1 EM-Algorithm -- 5.2 Results on Real Data -- 5.3 Prediction Results -- 6 Discussion -- References -- A New Multi-point Stepsize Gradient Method for Optimization -- 1 Introduction -- 2 MPSG Method -- 2.1 Quadratic Case -- 2.2 General Unconstrained Optimization -- 3 Extension to Extreme Eigenvalue Problems -- 4 Numerical Results -- 4.1 Quadratic Optimization Problems -- 4.2 Unconstrained Optimization Problems -- 4.3 Extreme Eigenvalue Problems -- References -- A Julia Implementation of Algorithm NCL for Constrained Optimization -- 1 Introduction -- 2 LANCELOT and NCL -- 3 Optimal Tax Policy Problems -- 4 Julia Implementation -- 4.1 Key Features -- 4.2 Implementation and Solver Features -- 4.3 Results with Julia/NCL on the Tax Policy Problems -- 4.4 Results with Julia/NCL on CUTEst Test Set -- 5 Nonlinear Least Squares -- 6 Summary -- 7 Detailed Results for Julia/NCL on NLS Problems -- References -- A Survey on Modeling Approaches for Generation and Transmission Expansion Planning Analysis -- 1 Introduction -- 2 Review of GTEP Models -- 2.1 Modeling Choices -- 2.2 Uncertainty Inclusion -- 2.3 High Level of Temporal Detail.; 3 A GTEP Model for the Decarbonization of Power Systems -- 4 Conclusions -- References -- Second Order Adjoints in Optimization -- 1 Introduction -- 2 Representation of First-Order Fréchet-Derivative -- 3 Representation of Second Order Fréchet-Derivative -- 4 Second Order Sensitivities and Second Order Adjoints -- 4.1 Sensitivity-Sensitivity Approach -- 4.2 Sensitivity-Adjoint Approach -- 4.3 Adjoint-Sensitivity Approach -- 4.4 Adjoint-Adjoint Approach -- 5 PDE-Constrained Optimization -- 6 Summary and Conclusions -- References -- Largest Small n-polygons: Numerical Optimum Estimates for n ≥ 6 -- 1 Introduction -- 2 A Standard Optimization Model for Finding LSP(n) -- 2.1 Model Formulation -- 2.2 Numerical Challenges -- 3 Related Earlier Studies -- 3.1 Analytical Approaches -- 3.2 Numerical Solution Approaches -- 3.3 The Asymptotic Behaviour of A(n) -- 4 Solving LSP Problems Numerically by AMPL-LGO -- 4.1 Solution Approach -- 4.2 The AMPL Model Development Environment -- 4.3 LGO Solver Suite for Nonlinear Optimization -- 5 Numerical Results and Comparisons -- 5.1 AMPL-LGO Results -- 5.2 An Illustrative Comparison with Results Obtained by Several AMPL Solvers -- 6 Regression Model Development -- 7 Concluding Remarks ; -- References -- Computational Science in the 17th Century. Numerical Solution of Algebraic Equations: Digit-by-Digit Computation -- 1 Introduction -- 2 Stevin's Method 1594 -- 3 Viète's Method 1600 -- 3.1 Pure Equations -- 3.2 Affected Equations -- 4 Test Examples from Harriot 1631 -- 5 Test Examples from Oughtred 1647/48 -- 6 On Newton's Annotations 1664 -- 7 Contributions of John Wallis 1685 -- 8 End of an Era -- 9 Computing the Square Root -- References -- NAOV-2020 Conference Participants.