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 Second Derivative SQP Method: Local Convergence and Practical Issues
SIAM Journal on Optimization
Infeasibility Detection and SQP Methods for Nonlinear Optimization
SIAM Journal on Optimization
A Primal-Dual Exterior Point Method for Nonlinear Optimization
SIAM Journal on Optimization
A new class of exact penalty functions and penalty algorithms
Journal of Global Optimization
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We propose two line search primal-dual interior-point methods for nonlinear programming that approximately solve a sequence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an ℓ2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, any limit point of the iterate sequence is either a Karush-Kuhn-Tucker (KKT) point of the barrier subproblem, or a Fritz-John (FJ) point of the original problem that fails to satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ); if the penalty parameter tends to infinity, there is a limit point that is either an infeasible FJ point of the inequality constrained feasibility problem (an infeasible stationary point of the infeasibility measure if slack variables are added) or a FJ point of the original problem at which the MFCQ fails to hold. Numerical results are given that illustrate these outcomes.