## Optimization Under Constraints: Theory and Applications of Nonlinear ProgrammingFirst thoughts on maximization; Constrained maximization and lagrangian methods; The strong lagrangian principle: convexity; Linear programming; Some particular linear problems; Some problems with linear constraints; Nonlinear constraints, and stochastic effects; Numerical methods; Vector maximization problems. |

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### Contents

First Thoughts on Maximization | 1 |

Constrained Maximization and Lagrangian Methods | 17 |

Convexity | 40 |

Copyright | |

9 other sections not shown

### Common terms and phrases

allocation problem amount argument assertion assumption attained basic bound boundary point characterization chosen co-ordinate coefficients concave concave function constant constrained maximization problem convex cone convex hull convex set corresponding cost denoted derivatives determined distribution dual problem efficient points elements equality constraints equilibrium point example Exercise exists expression extractor fact Figure finite flow follows framework given graph holds implies inequality interior interpretation interval inversion Lagrangian form Lagrangian methods Lagrangian multipliers Lagrangian theory linear programming load matrix maximizing f(x min-max theorem nodes non-negative scalar nonlinear orthant player positive prescribed probability problem of Section properties randomized solution recursion relation respect saddle-point satisfy sequence shadow price Show simplex method slack variables solution point stationary point strategy strong Lagrangian principle structure supporting hyperplane supporting hyperplane theorem Suppose supremum tion utility valid variables variation vector zero