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  This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. It includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems. Audience: The book can be a textbook or useful reference for undergraduate and graduate students in applied mathematics, operations research, and computer science.
Provides an introduction to the mathematical theory of optimization. Emphasizes the theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Recent developments are discussed.| Preface |
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xi | |
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1 | (22) |
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1 | (7) |
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8 | (7) |
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15 | (8) |
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23 | (18) |
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23 | (8) |
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31 | (2) |
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33 | (8) |
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41 | (10) |
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Unconstrained Optimization |
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42 | (1) |
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43 | (2) |
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45 | (6) |
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51 | (14) |
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Linearly Constrainted Optimization |
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51 | (3) |
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54 | (5) |
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Rosen's Gradient Projection Method |
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59 | (6) |
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65 | (16) |
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66 | (2) |
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A Property of Line Searches |
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68 | (4) |
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Consequences of the First Slope Lemma |
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72 | (9) |
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81 | (18) |
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81 | (4) |
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The Global Convergence of Rosen's Method |
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85 | (8) |
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93 | (6) |
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Inexact Active Constraints |
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99 | (26) |
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99 | (6) |
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105 | (7) |
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112 | (13) |
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125 | (8) |
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125 | (2) |
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127 | (3) |
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130 | (3) |
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133 | (18) |
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133 | (4) |
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137 | (6) |
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143 | (8) |
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151 | (16) |
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151 | (3) |
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154 | (7) |
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161 | (6) |
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167 | (20) |
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167 | (8) |
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175 | (3) |
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Solution of Gilbert-Pollak's Conjecture |
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178 | (9) |
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187 | (14) |
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Vertex Cover and MIN 2SAT |
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187 | (6) |
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193 | (2) |
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195 | (6) |
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201 | (14) |
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201 | (2) |
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203 | (2) |
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205 | (10) |
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215 | (12) |
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215 | (2) |
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Primal-Dual Affine Scaling |
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217 | (3) |
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220 | (7) |
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227 | (18) |
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228 | (1) |
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Global Optimization Approaches to Discrete Problems |
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229 | (1) |
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Nonconvex Quadratic Programming |
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230 | (15) |
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Concave Quadratic Programming |
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231 | (2) |
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233 | (8) |
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Indefinite Quadratic Programming |
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241 | (4) |
| Historical Notes |
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245 | (10) |
| Bibliography |
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255 | (16) |
| Index |
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271 | |
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