Optimal Quadratic Programming and QCQP Algorithms with Applications / by Zdeněk Dostál.

Format:

Book

Author/Creator:

Dostál, Zdeněk.

Series:

Springer Optimization and Its Applications, 1931-6836 ; 23

Language:

English

Subjects (All):

Mathematical optimization.

Calculus of variations.

Operations research.

Management science.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Numerical analysis.

Calculus of Variations and Optimization.

Operations Research, Management Science.

Mathematical and Computational Engineering Applications.

Numerical Analysis.

Local Subjects:

Calculus of Variations and Optimization.

Operations Research, Management Science.

Mathematical and Computational Engineering Applications.

Numerical Analysis.

Physical Description:

1 online resource (669 pages)

Edition:

2nd ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This 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.

Contents:

Preface

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031951671

OCLC:

1574117537