43 pages matching K-T conditions in this book
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The Nonlinear Programming Problem
Identifying an Optimal Point
14 other sections not shown
A(zk algorithmic map assume assumption barrier method basic variable calculate Chap closed map compact set concave function condition 2(b conjugate directions Consider continuous function continuously differentiable Convergence Theorem convergent subsequence convex function convex set convex-simplex method CSM-CD cutting-plane cutting-plane methods define definition determine dual problem eigenvectors ensures Equation example exercise exists feasible point feasible region Feasible-Direction Methods finite number given gradient Hessian matrix implies increase iteration k e Jf K-T conditions Lagrangean Lemma linear manifold map M1 matrix maximum negative NLP problem nonlinear programming number of steps objective function optimal for problem optimal point optimal solution partial derivatives point xk point-to-set map primal problem problem 8.1 problem max f(x Proof prove convergence pseudoconcave quasi-concave saddle point solution point solution test solve spacer step subproblem Suppose tableau tion vector verified xk+1 Z(zk