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Table of Contents

1 Optimization problems; introduction.- 1.1 Introduction.- 1.2 Transportation network.- 1.3 Production allocation model.- 1.4 Decentralized resource allocation.- 1.5 An inventory model.- 1.6 Control of a rocket.- 1.7 Mathematical formulation.- 1.8 Symbols and conventions.- 1.9 Differentiability.- 1.10 Abstract version of an optimal control problem.- References.- 2 Mathematical techniques.- 2.1 Convex geometry.- 2.2 Convex cones and separation theorems.- 2.3 Critical points.- 2.4 Convex functions.- 2.5 Alternative theorems.- 2.6 Local solvability and linearization.- References.- 3 Linear systems.- 3.1 Linear systems.- 3.2 Lagrangean and duality theory.- 3.3 The simplex method.- 3.4 Some extensions of the simplex method.- References.- 4 Lagrangean theory.- 4.1 Lagrangean theory and duality.- 4.2 Convex nondifferentiable problems.- 4.3 Some applications of convex duality theory.- 4.4 Differentiable problems.- 4.5 Sufficient Lagrangean conditions.- 4.6 Some applications of differentiable Lagrangean theory.- 4.7 Duality for differentiable problems.- 4.8 Converse duality.- References.- 5 Pontryagin theory.- 5.1 Introduction.- 5.2 Abstract Hamiltonian theory.- 5.3 Pointwise theorems.- 5.4 Problems with variable endpoint.- References.- 6 Fractional and complex programming.- 6.1 Fractional programming.- 6.2 Linear fractional programming.- 6.3 Nonlinear fractional programming.- 6.4 Algorithms for fractional programming.- 6.5 Optimization in complex spaces.- 6.6 Symmetric duality.- References.- 7 Some algorithms for nonlinear optimization.- 7.1 Introduction.- 7.2 Unconstrained minimization.- 7.3 Sequential unconstrained minimization.- 7.4 Feasible direction and projection methods.- 7.5 Lagrangean methods.- 7.6 Quadratic programming by Beale’s method.- 7.7 Decomposition.-References.- Appendices.- A.1 Local solvability.- A.2 On separation and Farkas theorems.- A.3 A zero as a differentiable function.- A.4 Lagrangean conditions when the cone has empty interior.- A.5 On measurable functions.- A.6 Lagrangean theory with weaker derivatives.- A.7 On convex functions.