An SQP method for mathematical programs with complementarity constraints with strong convergence properties
نویسندگان
چکیده
We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterate generated by our SQP method are at least M-stationary.
منابع مشابه
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints
Mathematical programs with nonlinear complementarity constraints are refor-mulated using better-posed but nonsmooth constraints. We introduce a class offunctions, parameterized by a real scalar, to approximate these nonsmooth prob-lems by smooth nonlinear programs. This smoothing procedure has the extrabenefits that it often improves the prospect of feasibility and stability...
متن کاملA Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints
The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results a...
متن کاملAn SQP method for mathematical programs with vanishing constraints with strong convergence properties
We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of [Formula: see text]-stationarity (Benko and Gfrerer in Optimization 66(1):61-92, 2017). We demonstrate how [Formula: see text]-stationary solutions of the quadratic program ...
متن کاملA Smoothing SQP Method for Mathematical Programs with Linear Second-Order Cone Complementarity Constraints∗
In this paper, we focus on the mathematical program with second-order cone (SOC) complementarity constraints, which contains the well-known mathematical program with nonnegative complementarity constraints as a subclass. For solving such a problem, we propose a smoothing-based sequential quadratic programming (SQP) methods. We first replace the SOC complementarity constraints with equality cons...
متن کاملAn Active Set Newton Method for Mathematical Programs with Complementarity
For mathematical programs with complementarity constraints (MPCC), we propose an active set Newton method which has the property of local quadratic convergence under the MPCC linear independence constraint qualification (MPCC-LICQ) and the standard second-order sufficient condition for optimality (SOSC). Under MPCC-LICQ, this SOSC is equivalent to the piecewise SOSC on branches of MPCC, which i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Kybernetika
دوره 52 شماره
صفحات -
تاریخ انتشار 2016