An Almost Feasible Sequential Linear Programming Algorithm

TL;DR

The novel method afSLP is shown to outperform FSLP and the state-of-the-art solver IPOPT on a SCARA robot optimization problem and includes enhancements to the originally proposed tolerance-tube method that are necessary for global convergence.

Abstract

This paper proposes an almost feasible Sequential Linear Programming (afSLP) algorithm. In the first part, the practical limitations of previously proposed Feasible Sequential Linear Programming (FSLP) methods are discussed along with illustrative examples. Then, we present a generalization of FSLP based on a tolerance-tube method that addresses the shortcomings of FSLP. The proposed algorithm afSLP consists of two phases. Phase I starts from random infeasible points and iterates towards a relaxation of the feasible set. Once the tolerance-tube around the feasible set is reached, phase II is started and all future iterates are kept within the tolerance-tube. The novel method includes enhancements to the originally proposed tolerance-tube method that are necessary for global convergence. afSLP is shown to outperform FSLP and the state-of-the-art solver IPOPT on a SCARA robot optimization problem.

Figures (7)

• Figure 1: Visual representation of Example \ref{['eq:example_feasibility_iterations']}.
• Figure 2: Illustration of Feasibility Iterations leading to an infeasible subproblem. Grayed-out areas are infeasible.
• Figure 3: Maximum trust-region radii for convergence of feasibility iterations with respect to the number of variables.
• Figure 4: Tolerance-tube around the feasible set $\mathcal{F}$. Grayed-out areas are infeasible.
• Figure 5: Cycling in the original tolerance-tube algorithm.