Dealing With Inconsistent Quadratic Programs in a SQP Based Algorithm

Abstract

In this paper we present a new sequential quadratic programming SQP algorithm that does not need any preprocessing phase. Its main features consist of not enforcing the Hessian to be positive definite and of dealing with infeasible QP problems in a novel way. The linearized constraints are analyzed and all those that do not belong to the minimal representation of the feasible region are eliminated. In the approach used the convergence rate of the algorithm may be adjusted by the user by properly selecting some tuning parameters that are also used to improve the robustness of the algorithm. The SQP code presented here is also able to deal with bound constraints that may be linearly dependent on the linearized equality or original constraints. The algorithm is shown to be robust and to perform well for small to medium-sized problem

PPD-IPM: Outer primal, inner primal-dual interior-point method for nonlinear programming

“…Typically this is achieved through 1penalties. This is sometimes referred to as elastic mode [11]. The 1 -penalties in the subproblem must be sufficiently large to ensure progress towards feasibility.…”

“…where θ depends only on ϑ, η, which in turn do not depend on k, ε. Thus, we can choose ε > 0 sufficiently small such that (11) and (12) contradict to each other. In only consequence, assumption (10) must be wrong.…”