Nonlinear ProgrammingMcGraw-Hill, 1969 - 220 pagine This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions. |
Sommario
To the Reader | 1 |
Linear Inequalities and Theorems | 16 |
Theorems of the alternative | 29 |
Copyright | |
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Applied assume assumption ball bounded called Chap chapter closed concave concave functions Consider constraint qualification containing continuous contradicts converse convex function convex set Corollary criterion definite denoted derive differentiable equivalent establish example exists fact feasible Find finite follows Fritz John g satisfies gi(x give given Hence holds implies inequality interior Kuhn-Tucker Lemma let g Let X limit linear linearly independent lower m-dimensional vector function Mathematics matrix maximum minimization problem nonlinear programming numerical function defined open set optimality criteria positive PROOF properties pseudoconcave pseudoconvex quasiconcave real number relations Remark require respect rg(x rows saddlepoint satisfy semicontinuous sequence Show solves strict strictly convex strictly quasiconvex sufficient optimality Theorem Let tion upper vector function weak zero