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Search Methods for Unconstrained Optimization
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assumed classical optimization complementary DFP concave function constrained local maximum constraint boundary constraint qualification convergence convex function convex set current point defined derivatives DFP method direction of search dynamic programming equality constraints equation evaluations Example f(xk function value given global maximum Golden Section search gradient methods Hence Hessian matrix inequality constraints initial point interval of uncertainty iteration Kuhn-Tucker necessary conditions Lagrange multipliers Lagrangian function linear programming linear programming problem linear searches maximum of f(x maximum value minimal path minimizes f(x minimizing problem minimum mutually conjugate directions node non-negativity restrictions nonlinear programming nonlinear programming problem objective function obtain optimal point optimal solution optimization problem optimization technique point x1 positive definite Powell's method problem 2.1 proof quadratic function quadratic programming problem replaced saddle-point satisfies the constraints search direction Section sequence solve step lengths Suppose surplus variables Theorem unconstrained optimization unrestricted in sign vector x'Dx