Foundations of optimization

I: Convex Analysis.- 1: Linear Subspaces and Affine Manifolds.- 1.1 Linear Subspaces and Orthogonal Complements.- 1.2 Linear Independence and Dimensionality.- 1.3 Projection Theorem.- 1.4 Affine Manifolds.- 2: Convex Sets.- 2.1 Convex Cones, Convex Sets and Convex Hills.- 2.2 Caratheodory Type Theorems.- 2.3 Relative Interior and Related Properties of Convex Sets.- 2.4 Support and Separation Theorems.- 3: Convex Cones.- 3.1 Cones, Convex Cones and Polar Cones.- 3.2 Polyhedral Cones.- 3.3 Cones Generated by Sets.- 3.4 Cone of Tangents.- 3.5 Cone of Attainable Directions, Cone of Feasible Directions and Cone of Interior Directions.- 4: Convex Functions.- 4.1 Definitions and Preliminary Results.- 4.2 Continuity and Directional Differentiability of Convex Functions.- 4.3 Differentiable Convex Functions.- 4.4 Some Examples of Convex Functions.- 4.5 Generalization of Convex Functions.- II: Optimality Conditions and Duality.- 5: Stationary Point Optimality Conditions with Differentiability.- 5.1 Inequality Constrained Problems.- 5.2 Inequality and Equality Constrained Problems.- 5.3 Optimality Criteria of the Minimum Principle Type.- 6: Constraint Qualifications.- 6.1 Inequality Constrained Problems.- 6.2 Equality and Inequality Constrained Problems.- 6.3 Necessary and Sufficient Qualification.- 7: Convex Programming without Differentiability.- 7.1 Saddle Point Optimality Criteria.- 7.2 Stationary Point Optimality Conditions.- 8: Lagrangian Duality.- 8.1 Definitions and Preliminary Results.- 8.2 The Strong Duality Theorem.- 9: Conjugate Duality.- 9.1 Closure of a Function.- 9.2 Conjugate Functions.- 9.3 Main Duality Theorem.- 9.4 Nonlinear Programming via Conjugate Functions.- Selected References.

著者

Bazaraa, Mokhtar S.、Shetty, C. M.、Bazaraa M. S.

出版社

Springer-Verlag

発売日

1976年1月発売

価格

価格未定（税込・書誌情報提供：openBD）

ISBN

9783540076803

発売済み