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This book gives an up-to-date presentation of the main algorithms for solving nonlinear continuous optimization (local and global methods), including linear programming as special cases linear programming (via simplex or interior point methods) and linear complementarity problems. Recently developed topics of parallel computation, neural networks for optimization, automatic differentiation and ABS methods are included. The book consists of 20 chapters written by well known specialists, who have made major contributions to developing the field. While a few chapters are mainly theoretical (as the one by Giannessi, which provides a novel, far-reaching approach to optimality conditions, and the one by Spedicato, which presents the unifying tool given by the ABS approach) most chapters have been written with special attention to features like stability, efficiency, high performance and software availability. The book will be of interest to persons with both theoretical and practical interest in the important field of optimization.
Preface. 1. General Optimality Conditions via a Separation Scheme; F. Giannessi. 2. Linear Equations in Optimization; C.G. Broyden. 3. Generalized and Sparse Least Squares Problems; Å. Björck. 4. Algorithms for Solving Nonlinear Systems of Equations; J.M. Martínez. 5. An Overview of Unconstrained Optimization; R. Fletcher. 6. Nonquadratic Model Methods in Unconstrained Optimization; Naiyang Deng, Zhengfeng Li. 7. Algorithms for General Constrained Nonlinear Optimization; M.C. Bartholomew-Biggs. 8. Exact Penalty Methods; G. Di Pillo. 9. Stable Barrier-Projection and Barrier-Newton Methods for Linear and Nonlinear Programming; Y.G. Evtushenko, V.G. Zhadan. 10. Large-Scale Nonlinear Constrained Optimization: a Current Survey; A.R. Conn, N. Gould, P.L. Toint. 11. ABS Methods for Nonlinear Optimization; E. Spedicato, Zunquan Xia. 12. A Condensed Introduction to Bundle Methods in Nonsmooth Optimization; C. Lemaréchal, J. Zowe. 13. Computational Methods for Linear Programming; D.F. Shanno. 14. Infeasible Interior Point Methods for Solving Linear Programs; J. Stoer. 15. Algorithms for Linear Complementarity Problems; J.J. Júdice. 16. A Homework Exercise — the 'Big M' Problem; R.W.H. Sargent. 17. Deterministic Global Optimization; Y.G. Evtushenko, M.A. Potapov. 18. On Automatic Differentiation and Continuous Optimization; L.C.W. Dixon. 19. Neural Networks and Unconstrained Optimization; L.C.W. Dixon. 20. Parallel Nonlinear Optimization: Limitations, Challenges and Opportunities; R.B. Schnabel. 21. Index.
Overview
This book gives an up-to-date presentation of the main algorithms for solving nonlinear continuous optimization (local and global methods), including linear programming as special cases linear programming (via simplex or interior point methods) and linear complementarity problems. Recently developed topics of parallel computation, neural networks for optimization, automatic differentiation and ABS methods are included. The book consists of 20 chapters written by well known specialists, who have made major ...