Sequential Linear Programming With Adaptive Linearization Error Limits for All-Time Feasibility

Abstract

This letter presents an enhanced Trust Region Method (TRM) for Sequential Linear Programming (SLP) designed to improve the initial feasible solution to a constrained nonlinear programming problem while maintaining the interim solutions feasibility throughout the SLP iterations. The method employs a polytopic sub-approximation of the feasible region, defined around the interim solution as a level set based on variable limits for the linearization error. This polytopic feasible region is established by using a trust region that ensures that maximum limits of the linearization errors are respected. The method adaptively adjusts the size of the feasible region during iterations to achieve convergence to a local optimum by employing variable linearization error limits. Local convergence is attained by reducing the size of the trust radius. A case study illustrates the effectiveness of the proposed method, which is compared to the benchmark TRM that uses heuristic limits on the permissible changes in manipulated variables.