Foundations of OptimizationThis book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with. |
Contents
| 1 | |
2 Unconstrained Optimization | 31 |
3 Variational Principles | 61 |
4 Convex Analysis | 84 |
5 Structure of Convex Sets and Functions | 117 |
6 Separation of Convex Sets | 140 |
7 Convex Polyhedra | 175 |
8 Linear Programming | 194 |
11 Duality Theory and Convex Programming | 274 |
12 Semiinfinite Programming | 313 |
13 Topics in Convexity | 335 |
14 Three Basic Optimization Algorithms | 361 |
A Finite Systems of Linear Inequalities in VectorSpaces | 407 |
B Descartess Rule of Sign | 413 |
C Classical Proofs of the Open Mapping and Gravess Theorems | 416 |
| 421 | |
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Common terms and phrases
affine algebraic algorithms apply approach assume Banach spaces bounded called Chapter claim closed compact cone Consequently Consider constraint contains continuous contradiction convergence convex function convex set Corollary Define derivative determine differentiable direction dual duality ellipsoid equality equation equivalent example exists fact feasible finite follows formula function f given gives global minimizer holds hyperplane implies important independent inequality KKT conditions KKT points Lagrangian Lemma Let f linear program matrix maximizer means method multipliers neighborhood nonempty Note obtain optimal optimal solution optimality conditions optimization problem origin polynomial possible problem Proof properties prove quadratic rai(C Remark respectively result satisfying separation sequence Show solving strictly subset sufficient Suppose symmetric symmetric matrix Theorem theory tion variable variational vector space write zero