Hybrid Filter Trust Region Algorithm Based Upon SLP Combined With SQP For Nonlinear Optimization Problem

In this paper, nonlinear constrained optimization problems are taken into consideration. The motivation of this paper is attempt to design a simple, effective hybrid algorithm for complexity and large-scale optimization models, and some modifications were done on SLP-EQP method introduced by Chin and Fletcher (2003). This paper constructs a new algorithm on the basis of SLP model with auxiliary SQP, trust region technique, and the latest filter concept:(1) We find the iterative direction by solving a new RTR sub-problem produced by the combination of SLP model, Robinson’s method, and the trust region. (2)If the iterative direction of RTR is not satisfied for the filter acceptance criterion, then we solve another EQP sub-problem formed by mixing SLP with SQP. This new direction of EQP is much better than that of SLP only. (3) If the direction of EQP is again not satisfied for the filter acceptance criterion, then using the idea of dogleg method, we yield a new direction by combining the Cauchy direction with RTR direction. (4)If this new direction is not satisfied for the filter acceptance criterion, we choose its projective stepdp. Via the above four procedures, we can obtain an effective and modified algorithm for solving modern optimization problems. On the other hand, the linear approximation of the constraints may lead to inconsistent of the SLP sub-problem, a feasibility restoration phase would be proceeded. Here we add the Tolerant technology proposed first by Powell (1989) to expand the solubility of SLP. Under some conventional assumptions, we prove the global convergence of the new algorithm. Moreover, a large number of numerical experiments show that the new algorithm is effective.