## Duality in Optimization and Variational InequalitiesThis comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems. |

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### Contents

Duality in Network Optimization | 41 |

FIGURE CAPTIONS | 43 |

Chapters Duality in Linear Systems | 93 |

Duality in Convex Nonlinear Systems | 127 |

Duality in Nonconvex Systems | 151 |

Duality in Variational Inequalities | 193 |

Chapter? Elements of Multicriteria Optimization | 215 |

Chapters Duality in Multicriteria Optimization | 237 |

Duality in Vector Variational Inequalities | 267 |

293 | |

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### Common terms and phrases

algorithm Assume assumption Chapter column compute concave concave function constraint convex cone convex function convex optimization convex set Corollary corresponding cotree arc cut Q cycle Definition differentiable dual function dual problem duality result duality theorem exists Farkas Lemma feasible flow feasible potential feasible solution Fenchel transform finite gap function given hence hyperplane implies incidence matrix inf max infeasible infimum int Rp kilter curve Lagrangian Lagrangian function Lemma linear programming matrix max flow minimum monotone function monotropic multicriteria optimization problem node nonempty optimal flow optimal solution optimality condition painted network path perturbation function primal and dual primal problem Proof properly minimal properties Rpxn saddle point satisfies scalar set-valued function simplex algorithm solves spanning tree strong duality subgradient subset supporting hyperplane type I convex vector variational inequality vector-valued function weak duality weakly minimal solution zero duality gap

### References to this book

Vector Optimization: Set-valued and Variational Analysis Guang-ya Chen,Xuexiang Huang,Xiaogi Yang Limited preview - 2005 |