Semismooth Newton Methods for Solving Semi-Infinite Programming Problems
Journal of Global Optimization
A Smoothing Newton Method for Semi-Infinite Programming
Journal of Global Optimization
Computational Optimization and Applications
Quasi-Newton acceleration for equality-constrained minimization
Computational Optimization and Applications
Improving ultimate convergence of an augmented Lagrangian method
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Low Order-Value Optimization and applications
Journal of Global Optimization
Journal of Computational and Applied Mathematics
A feasible descent SQP algorithm for general constrained optimization without strict complementarity
Journal of Computational and Applied Mathematics
Second-order negative-curvature methods for box-constrained and general constrained optimization
Computational Optimization and Applications
Computational Optimization and Applications
Low order-value approach for solving VaR-constrained optimization problems
Journal of Global Optimization
A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences
SIAM Journal on Optimization
Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization
Computational Optimization and Applications
Handling infeasibility in a large-scale nonlinear optimization algorithm
Numerical Algorithms
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In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian--Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush--Kuhn--Tucker (KKT) points is a KKT point if the CPLD holds there. We show that a KKT point satisfying the CPLD and the strong second-order sufficiency conditions (SSOSC) is an isolated KKT point. We then establish convergence of a general sequential quadratical programming (SQP) method under the CPLD and the SSOSC. Finally, we apply these results to analyze the feasible SQP method proposed by Panier and Tits in 1993 for inequality constrained optimization problems. We establish its global convergence under the SSOSC and a condition slightly weaker than the Mangasarian--Fromovitz constraint qualification, and we prove superlinear convergence of a modified version of this algorithm under the SSOSC and a condition slightly weaker than the linear independence constraint qualification.