A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Lagrange methods for finding degenerate solutions of conditional extremum problems
Computational Mathematics and Mathematical Physics
Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution
Computational Optimization and Applications
Exact Penalization of Mathematical Programs with Equilibrium Constraints
SIAM Journal on Control and Optimization
Stabilized Sequential Quadratic Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Modified Wilson'S Method for Nonlinear Programswith Nonunique Multipliers
Mathematics of Operations Research
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems
Computational Optimization and Applications
Mathematics of Operations Research
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Optimality Conditions for Irregular Inequality-Constrained Problems
SIAM Journal on Control and Optimization
On the Accurate Identification of Active Constraints
SIAM Journal on Optimization
Complementarity Constraint Qualification via the Theory of 2-Regularity
SIAM Journal on Optimization
Modifying SQP for Degenerate Problems
SIAM Journal on Optimization
Mathematics of Operations Research
Newton-Type Methods for Optimization Problems without Constraint Qualifications
SIAM Journal on Optimization
SIAM Journal on Optimization
An Algorithm for Degenerate Nonlinear Programming with Rapid Local Convergence
SIAM Journal on Optimization
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
Optimality Conditions: Abnormal and Degenerate Problems (Mathematics and its Applications Volume 526)
Mathematical Programming: Series A and B
On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions
Mathematical Programming: Series A and B
Sharp Primal Superlinear Convergence Results for Some Newtonian Methods for Constrained Optimization
SIAM Journal on Optimization
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We discuss possible scenarios of behaviour of the dual part of sequences generated by primal-dual Newton-type methods when applied to optimization problems with nonunique multipliers associated to a solution. Those scenarios are: (a) failure of convergence of the dual sequence; (b) convergence to a so-called critical multiplier (which, in particular, violates some second-order sufficient conditions for optimality), the latter appearing to be a typical scenario when critical multipliers exist; (c) convergence to a noncritical multiplier. The case of mathematical programs with complementarity constraints is also discussed. We illustrate those scenarios with examples, and discuss consequences for the speed of convergence. We also put together a collection of examples of optimization problems with constraints violating some standard constraint qualifications, intended for preliminary testing of existing algorithms on degenerate problems, or for developing special new algorithms designed to deal with constraints degeneracy.