SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
A robust sequential quadratic programming method
Mathematical Programming: Series A and B
A numerical approach to optimization problems with variational inequality constraints
Mathematical Programming: Series A and B
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints
Mathematical Programming: Series A and B
Stability of regularized bilevel programming problems
Journal of Optimization Theory and Applications
Computational Optimization and Applications
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution
Computational Optimization and Applications
Stabilized Sequential Quadratic Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Degenerate Nonlinear Programming with a Quadratic Growth Condition
SIAM Journal on Optimization
Optimality Conditions for Optimization Problems with Complementarity Constraints
SIAM Journal on Optimization
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints
SIAM Journal on Optimization
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This paper discusses a special class of mathematical programs with nonlinear complementarity constraints, its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. We first reformulate the complementarity constraints as a standard nonlinear equality and inequality constraints by making use of a class of generalized smoothing complementarity functions, then present a new SQP algorithm for the discussed problems. At each iteration, with the help of a pivoting operation, a master search direction is yielded by solving a quadratic program, and a correction search direction for avoiding the Maratos effect is generated by an explicit formula. Under suitable assumptions, without the strict complementarity on the upper-level inequality constraints, the proposed algorithm converges globally to a B-stationary point of the problems, and its convergence rate is superlinear.