Feasible direction interior-point technique for nonlinear optimization

作     者：Herskovits, J 

作者机构：Univ Fed Rio de Janeiro COPPE Mech Engn Program BR-21945 Rio De Janeiro Brazil 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：1998年第99卷第1期

页      面：121-146页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：nonlinear constrained optimization interior-point methods feasible direction algorithms 

摘      要：We propose a feasible direction approach for the minimization by interior-point algorithms of a smooth function under smooth equality and inequality constraints. It consists of the iterative solution in the primal and dual variables of the Karush-Kuhn-Tucker first-order optimality conditions. At each iteration, a descent direction is defined by solving a linear system. In a second stage, the linear system is perturbed so as to deflect the descent direction and obtain a feasible descent direction. A line search is then performed to get a new interior point and ensure global convergence. Based on this approach, first-order, Newton, and quasi-Newton algorithms can be obtained. To introduce the method, we consider first the inequality constrained problem and present a globally convergent basic algorithm. Particular first-order and quasi-Newton versions of this algorithm are also stated. Then, equality constraints are included. This method, which is simple to code, does not require the solution of quadratic programs and it is neither a penalty method nor a barrier method. Several practical applications and numerical results show that our method is strong and efficient.