Methods of OptimizationNonlinear programming. Kuhn-tucker necessary conditions. Saddle-point property of the lagrangian functions. The constraint qualification. Search methods for unconstrained optimization. Grild search. Hooke and jeeves' method. Spendley, hext and himsworth's method. Nelder and mead's method. Gradient methods for unconstrained optimization. Method of steepest descent. The newton-raphson method. The davidon-fletcher-powell method. Constrained optimization. Hemstitching. The gradient projection method. Penalty functions. Dynamic programming The allocation problem. Oriented networks. The farmer's problem. |
Contents
Introduction | 1 |
Nonlinear Programming | 35 |
Search Methods for Unconstrained Optimization | 74 |
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b₁ b₂ complementary DFP concave function constrained local maximum constraint boundary constraint qualification convex function convex set current point d₂ defined DFP method direction of search dynamic programming equality constraints equation evaluations Example function f(x function value g₁ given global maximum Golden Section search gradient methods H₁ h₂ Hence Hessian matrix inequality constraints initial point Kuhn-Tucker necessary conditions Lagrange multipliers Lagrangian function linear programming linear programming problem linear searches local maximum matrix maximize Maximize z maximum of f(x maximum value minimal path minimizes f(x minimum mutually conjugate directions node non-negativity restrictions nonlinear programming nonlinear programming problem objective function obtain optimal point optimal solution optimization problem optimization technique positive definite Powell's method problem 2.1 proof quadratic function quadratic programming quadratic programming problem saddle-point search direction Section solve step lengths surplus variables Theorem unconstrained optimization vector x'Dx x₁ x₁² x₂