A smoothing SQP method for nonlinear programs with stability constraints arising from power systems

Abstract

This paper investigates a new class of optimization problems arising from power systems, known as nonlinear programs with stability constraints (NPSC), which is an extension of ordinary nonlinear programs. Since the stability constraint is described generally by eigenvalues or norm of Jacobian matrices of systems, this results in the semismooth property of NPSC problems. The optimal conditions of both NPSC and its smoothing problem are studied. A smoothing SQP algorithm is proposed for solving such optimization problem. The global convergence of algorithm is established. A numerical example from optimal power flow (OPF) is done. The computational results show efficiency of the new model and algorithm.

Smoothing SQP Methods for Solving Degenerate Nonsmooth Constrained Optimization Problems with Applications to Bilevel Programs

“…Recently [22,40] extended the result of [44] to a class of nonsmooth constrained optimization problem using the projected gradient method and the augmented Lagrangian method respectively. Smoothing functions are proposed and the SQP method has been used for the smooth problem in [15,21] to solve the mathematical programs with complementarity constraints (MPCC) and in [23,37] to solve the semi-infinite programming (SIP). In this paper we will combine the SQP method and the smoothing technique to design a smoothing SQP method for a class of general constrained optimization problems with smoothing functions satisfying the gradient consistency property.…”