يك روش برنامه‌ريزي درجه دوم دنباله‌اي فيلتر غيريكنوا: همگرايي و نتايج عددي

A Nonmonotone Filter SQP Method: Connvergence an‎d Numerical Results

رياضي كاربردي و علوم كامپيوتر

Constrained nonlinear optimization has become an indispensable tool in many scientific an‎d engineering applications, where the objective is to determine an optimal solution while satisfying a set of equality an‎d inequality constraints. The increasing complexity an‎d non-convexity of practical optimization problems have motivated the development of robust numerical methods capable of balancing objective reduction an‎d feasibility improvement throughout the optimization process. In this thesis, two closely related filter-based sequential quadratic optimization methods were studied for solving general nonlinear constrained optimization problems. The first part focused on a filter line-search algorithm with unified step computation, in which every search direction was obtained by solving computationally tractable optimization subproblems that remained feasible throughout the iterative process. Unlike conventional filter methods that require a separate restoration phase to recover feasibility, the proposed framework integrated feasibility restoration an‎d objective reduction within a unified computational procedure through the use of exact penalty models an‎d quadratic programming techniques. The second part of the thesis examined a nonmonotone extension of the unified filter algorithm. By relaxing the strict monotonicity requirements imposed by the filter acceptance mechanism, the nonmonotone strategy allowed the acceptance of selec‎ted intermediate iterates without sacrificing the global convergence properties established for the original method. Furthermore, the local convergence behavior of the algorithm was investigated, an‎d its superlinear convergence under stan‎dard regularity assumptions was presented. The numerical results reported in the corresponding study were also reviewed, demonstrating that the nonmonotone strategy achieved an effective compromise between the quality of accepted steps an‎d the overall computational efficiency. Finally, the theoretical framework, mathematical models, convergence properties, an‎d algorithmic structures of both methods were analyzed an‎d compared. The study showed that integrating unified step computation with a nonmonotone filter strategy provides a reliable an‎d efficient framework for solving nonlinear an‎d nonconvex constrained optimization problems while eliminating the need for a separate restoration phase an‎d improving the overall performance of filter-based sequential quadratic optimization methods.

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