A New Superlinearly Convergent Algorithm of Combining QP Subproblem with System of Linear Equations for Nonlinear Optimization

TL;DR

This paper introduces a new superlinearly convergent algorithm for nonlinear optimization with inequality constraints, combining quadratic programming subproblems and linear systems, which is globally convergent and efficient.

Contribution

It proposes a novel algorithm that ensures superlinear convergence and feasibility for nonlinear constrained optimization by integrating QP subproblems with linear equations.

Findings

Algorithm achieves superlinear convergence.

Initial point can be arbitrarily chosen.

Preliminary experiments show promising results.

Abstract

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly convergent algorithm is proposed. The initial iteration point can be chosen arbitrarily for the algorithm. At each iteration, the new algorithm solves one quadratic programming subproblem which is always feasible, and one or two systems of linear equations with a common coefficient matrix. Moreover, the coefficient matrix is uniformly nonsingular. After finite iterations, the iteration points can always enter into the feasible set of the problem, and the search direction is obtained by solving one quadratic programming subproblem and only one system of linear equations. The new algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some preliminary numerical experiments are reported to show that the algorithm is promising.