30954470X - Nonlinear Programming S ECOND EDITION D imitri...

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Nonlinear Programming SECOND EDITION Dimitri P. Bertsekas Massachusetts Institute of Technology WWW site for book Information and Orders http://world.std.com/~athenasc/index.html Athena Scientific, Belmont, Massachusetts
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Contents 1. Unconstrained Optimization p. 1 1.1. Optimality Conditions p. 4 1.1.1. Variational Ideas 1.1.2. Main Optimality Conditions p. 13 1.2. Gradient Methods - Convergence p. 22 1.2.1. Descent Directions and Stepsize Rules p. 22 1.2.2. Convergence Results p. 43 1.3. Gradient Methods - Rate of Convergence p. 62 1.3.1. The Local Analysis Approach p. 64 1.3.2. The Role of the Condition Number p. 65 1.3.3. Convergence Rate Results p. 75 1.4. Newton's Method and Variations p. 88 1.5. Least Squares Problems p. 102 1.5.1. The Gauss-Newton Method p. 107 1.5.2. Incremental Gradient Methods* p. 108 1.5.3. Incremental Forms of the Gauss-Newton Method* ... . p. 119 1.6. Conjugate Direction Methods p. 130 1.7. Quasi-Newton Methods p. 148 1.8. Nonderivative Methods p. 158 1.8.1. Coordinate Descent p. 160 1.8.2. Direct Search Methods p. 162 1.9. Discrete-Time Optimal Control Problems* p. 166 1.10. Some Practical Guidelines p. 183 1.11. Notes and Sources p. 187 2. Optimization Over a Convex Set p. 191 2.1. Optimality Conditions p. 192 2.2. Feasible Directions and the Conditional Gradient Method . . p. 209 2.2.1. Descent Directions and Stepsize Rules p. 210 2.2.2. The Conditional Gradient Method p. 215 2.3. Gradient Projection Methods p. 223 2.3.1. Feasible Directions and Stepsize Rules Based on Projection p. 223 v
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vi Contents 2.3.2. Convergence Analysis*
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This note was uploaded on 05/12/2011 for the course INDUSTRIAL 321 taught by Professor Memet during the Spring '11 term at Mitchell Technical Institute.

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30954470X - Nonlinear Programming S ECOND EDITION D imitri...

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