سخنرانی کلیدی شماره 5 سخنرانی کلیدی با عنوان "A competitive inexact non-monotone filter sequential quadratic programming algorithm" توسط دکتر نظام الدین مهدوی امیری استاد تمام دانشگاه صنعتی شریف

Nezam Mahdavi-Amiri and Hani Ahmadzadeh
Sharif University of Technology
nezamm@sharif.edu

Abstract In solving smooth constrained nonlinear optimization problems,the use of Sequential Quadratic Programming (SQP) algorithms has shown to be successful, mainly because of fast rate of local convergence. Solving successive SQP problems is costly,however,due to the engagement of all the constraints in every iteration. This effectively makes the SQP methods be practical merely on small and possibly on medium problems. Inexact SQP algorithms have recently been considered to enhance the performance of SQP methods. Here,we devise a new inexact SQP algorithm as follows. When an infeasible iterate is at hand (outer iteration),two directions are computed. First,a so-called steering direction is computed,minimizing a linear approximation of the constraint violations in a trust region. Then,using the steering direction,a so-called predictor direction is computed as an inexact solution of a quadratic programming problem,while being a descent direction for the penalty function. An overall search direction,constructed by a convex combination of the steering and predictor directions,is enforced to be descent for the constraint violations. By an appropriate updating of the penalty parameter,the search direction is also made to be a descent direction for the exact penalty function. When a feasible iterate is at hand (inner iteration),by solving a convex quadratic model inexactly,a descent direction for the objective function is computed. A non-monotone filter strategy is employed to avoid the Maratos effect. The global convergence and superlinear local rate of convergence of the algorithm are established under some standard assumptions. Competitive numerical results of an implementation of our algorithm,in comparison with the state-of-the-art SQP algorithms,are reported

Key words: Nonlinear optimization,Sequential quadratic programming,Exact penalty function,Inexact algorithm,Non-monotone algorithm,Filter.

بازگشت

1398/11/26