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. Language: English