Introduction to Global OptimizationSpringer US, 31 thg 10, 2000 - 354 trang In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P.M. Pardalos and N.V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith mic, and computational contributions have helped to solve globally multi extreme problems arising from important practical applications. |
Nội dung
Complexity of KuhnTuckerPoints in Quadratic Pro | 34 |
Quadratic Programming | 43 |
3 | 67 |
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Introduction to Global Optimization R. Horst,Panos M. Pardalos,Nguyen Van Thoai Xem trước bị giới hạn - 1995 |
Introduction to Global Optimization R. Horst,Panos M. Pardalos,Nguyen Van Thoai Xem trước bị giới hạn - 2000 |
Introduction to Global Optimization R. Horst,Panos M. Pardalos,Nguyen Van Thoai Xem trước bị giới hạn - 1995 |
Thuật ngữ và cụm từ thông dụng
affine function assume bound algorithm branch and bound Compute concave function concave minimization problem Consider constraints convex envelope convex function convex set corresponding d.c. program defined denote edge equivalent example feasible domain feasible point feasible set fi(x finite number function f(x given global minimum global optimization hence hyperplane H inequality integer intersection iteration Kuhn-Tucker linear program linearly independent Lipschitz lower bound matrix maximum clique maximum clique problem min{f(x n-simplex node nonconvex nonempty nonlinear NP-complete NP-hard objective function objective function value obtain optimal solution optimal value optimization problems outer approximation partition sets piecewise linear polynomial polytope problem min f(x programming problem Proof Proposition quadratic problem quadratic programming R₁ rectangle satisfying Section sequence simplex solving subdivision subproblem Theorem upper bound v₁ variables vector vertex vertex set vertices y-extension zero-one