Nonlinear Programming: A Unified Approach |
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Contents
The Nonlinear Programming Problem | 2 |
Identifying an Optimal Point | 22 |
Applications of the KuhnTucker Conditions and Duality Theory | 62 |
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Common terms and phrases
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 convex set convex-simplex method CSM-CD cutting-plane methods d₁ define definition determine dual problem Equation exercise exists feasible point feasible region Feasible-Direction Methods finite number given gradient Hessian matrix holds iteration K-T conditions Lagrangean Lemma linear M¹(x manifold map M¹ matrix maximize maximum negative semidefinite NLP problem nonlinear programming number of steps objective function optimal for problem optimal point optimal solution pivot point-to-set map problem 8.1 procedure PROOF prove convergence pseudoconcave quadratic quasi-concave saddle point satisfies sequence solution point solve spacer step subproblem Suppose tableau vector verified Vf(x Vƒ(x x*+¹ xk+1 Z function zero zk+1