Convex Analysis and Global OptimizationSpringer Science & Business Media, 9 thg 3, 2013 - 340 trang Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization. |
Nội dung
5 | 56 |
MOTIVATION AND OVERVIEW | 109 |
ст | 131 |
Procedure DC | 140 |
Rectangular Algorithms | 159 |
OUTER AND INNER APPROXIMATION | 177 |
DECOMPOSITION | 223 |
NONCONVEX QUADRATIC | 277 |
| 319 | |
| 337 | |
Ấn bản in khác - Xem tất cả
Thuật ngữ và cụm từ thông dụng
accumulation point affine function affine set assume basic optimal solution branch and bound closed convex set compute concave function concave minimization convergence convex cone convex minorant convex program convex set Corollary d.c. function defined Denote exists extreme point f(xº feasible point feasible solution fi(x finite follows function f(x global minimizer global optimal global optimal solution halfline hence hyperplane implies inequality inf{f(x intC iteration K₁ Lemma linear program lower bound LRCP M₁ matrix method min{f(x nonempty objective function optimal value optimization problems outer approximation P₁ partition Pk+1 polyhedron polytope Procedure DC Proof Let proper convex function Proposition quadratic function quasiconcave quasiconvex rectangle relative interior reverse convex satisfying sequence simplex solving Step subdivision subset Theorem vector vertex set