A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
A superlinear infeasible-interior-point algorithm for monotone complementarity problems
Mathematics of Operations Research
Stationary points of bound constrained minimization reformulations of complementarity problems
Journal of Optimization Theory and Applications
Primal-dual interior-point methods
Primal-dual interior-point methods
New constrained optimization reformulation of complementarity problems
Journal of Optimization Theory and Applications
Interfaces to PATH 3.0: Design, Implementation and Usage
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
On the Resolution of the Generalized Nonlinear Complementarity Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
Mathematical Programming: Series A and B
On the natural merit function for solving complementarity problems
Mathematical Programming: Series A and B
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Interior---point algorithms are among the most efficient techniques for solving complementarity problems. In this paper, a procedure for globalizing interior---point algorithms by using the maximum stepsize is introduced. The algorithm combines exact or inexact interior---point and projected---gradient search techniques and employs a line---search procedure for the natural merit function associated with the complementarity problem. For linear problems, the maximum stepsize is shown to be acceptable if the Newton interior---point search direction is employed. Complementarity and optimization problems are discussed, for which the algorithm is able to process by either finding a solution or showing that no solution exists. A modification of the algorithm for dealing with infeasible linear complementarity problems is introduced which, in practice, employs only interior---point search directions. Computational experiments on the solution of complementarity problems and convex programming problems by the new algorithm are included.