LEADER 04490nam 22006975 450 001 9911035053603321 005 20251028120408.0 010 $a9783031951671 024 7 $a10.1007/978-3-031-95167-1 035 $a(CKB)41827035400041 035 $a(MiAaPQ)EBC32378986 035 $a(Au-PeEL)EBL32378986 035 $a(DE-He213)978-3-031-95167-1 035 $a(EXLCZ)9941827035400041 100 $a20251028d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal Quadratic Programming and QCQP Algorithms with Applications /$fby Zden?k Dostál 205 $a2nd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (669 pages) 225 1 $aSpringer Optimization and Its Applications,$x1931-6836 ;$v23 311 08$a9783031951664 327 $aPreface -- Part I Background -- Chapter 1 Linear Algebra -- Chapter 2 Optimization -- Part II Basic Algorithms -- Chapter 3 Gradient Methods -- Chapter 4 Conjugate Gradients as Direct Method -- Chapter 5 Gradient Projection -- Chapter 6 From Penalty to Exact Augmented Lagrangians -- Chapter 7 Active Sets with Finite Termination -- Part III Optimal Algorithms -- Chapter 8 Conjugate Gradients as Iterative Method -- Chapter 9 SMALE for Equality Constraints -- Chapter 10 MPRGP for Bound Constraints -- Chapter 11 MPGP and PBBF for Separable QCQP -- Chapter 12 Solvers for Separable and Equality QP/QCQP Problems -- Part IV Case Studies -- Chapter 13 Elliptic Variational Inequalities -- Chapter 14 Contact Problem with Friction -- Chapter 15 Model Predictive Control -- Chapter 16 Support Vector Machines -- Chapter 17 PERMON and ESPRESO Software -- References. 330 $aThis book presents cutting-edge algorithms for solving large-scale quadratic programming (QP) and/or QPSQP. While applying these algorithms to the class of QP problems with the spectrum confined to a positive interval, the theory guarantees finding the prescribed precision solution through a uniformly bounded number of simple iterations, like matrix-vector multiplications. Key concepts explored include the active set strategy, spectral gradients, and augmented Lagrangian methods. The book provides a comprehensive quantitative convergence theory, avoiding unspecified constants. Through detailed numerical experiments, the author demonstrates the algorithms' superior performance compared to traditional methods, especially in handling large problems with sparse Hessian. The performance of the algorithms is shown on large-scale (billions of variables) problems of mechanics, optimal control, and support vector machines. Ideal for researchers and practitioners in optimization and computational mathematics, this volume is also an introductory text and a reference for advanced studies in nonlinear programming. Whether you're a scholar in applied mathematics or an engineer tackling complex optimization challenges, this book offers valuable insights and practical tools for your work. 410 0$aSpringer Optimization and Its Applications,$x1931-6836 ;$v23 606 $aMathematical optimization 606 $aCalculus of variations 606 $aOperations research 606 $aManagement science 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aNumerical analysis 606 $aCalculus of Variations and Optimization 606 $aOperations Research, Management Science 606 $aMathematical and Computational Engineering Applications 606 $aNumerical Analysis 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aOperations research. 615 0$aManagement science. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aNumerical analysis. 615 14$aCalculus of Variations and Optimization. 615 24$aOperations Research, Management Science. 615 24$aMathematical and Computational Engineering Applications. 615 24$aNumerical Analysis. 676 $a519.6 676 $a515.64 700 $aDosta?l$b Zdene?k$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911035053603321 996 $aOptimal Quadratic Programming and QCQP Algorithms with Applications$94451920 997 $aUNINA