Steering exact penalty methods for nonlinear programming
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
A Complementarity Constraint Formulation of Convex Multiobjective Optimization Problems
INFORMS Journal on Computing
On the asymmetric eigenvalue complementarity problem
Optimization Methods & Software - GLOBAL OPTIMIZATION
Infeasibility Detection and SQP Methods for Nonlinear Optimization
SIAM Journal on Optimization
A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
An $\ell_1$ Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints
SIAM Journal on Optimization
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This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then extended to an interior-relaxation approach. Superlinear convergence to strongly stationary points is also established. Two strategies for updating the penalty parameter are proposed, and their efficiency and robustness are studied on an extensive collection of test problems.