This 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.
1. Mathematical Preliminaries 2. Duality in Network Optimization 3. Duality in Linear Systems 4. Duality in Convex Nonlinear Systems 5. Duality in Nonconvex Systems 6. Duality in Variational Inequalities 7. Elements of Multicriteria Optimization 8. Duality in Multicriteria Optimization 9. Duality in Vector Variational Inequalities