Trajectory-following algorithms for min-max optimization problems
Journal of Optimization Theory and Applications
New minimax inequality with applications to existence theorems of equilibrium points
Journal of Optimization Theory and Applications
Minimax theorems and cone saddle points of uniformly same-order vector-valued functions
Journal of Optimization Theory and Applications
Asynchronous parallel methods for enclosing solutions of nonlinear equations
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
General models in min-max continuous location: theory and solution techniques
Journal of Optimization Theory and Applications
Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations
Journal of Computational and Applied Mathematics
New constrained optimization reformulation of complementarity problems
Journal of Optimization Theory and Applications
Min-max optimization of several classical discrete optimization problems
Journal of Optimization Theory and Applications
Multiple-load truss topology and sizing optimization: some properties of minimax compliance
Journal of Optimization Theory and Applications
Convergence of partially asynchronous block quasi-Newton methods for nonlinear systems of equations
Journal of Computational and Applied Mathematics
Globally convergent inexact generalized Newton's methods for nonsmooth equations
Journal of Computational and Applied Mathematics
Minimax results and finite-dimensional separation
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
A modification of Newton's method for nondifferentiable equations
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
A differential evolution approach for solving constrained min-max optimization problems
Expert Systems with Applications: An International Journal
Hi-index | 0.00 |
In this paper, reference variable methods are proposed for solving nonlinear Minmax optimization problems with unconstraint or constraints for the first time, it uses reference decision vectors to improve the methods in Vincent and Goh (J Optim Theory Appl 75:501---519, 1992) such that its algorithm is convergent. In addition, a new method based on KKT conditions of min or max constrained optimization problems is also given for solving the constrained minmax optimization problems, it makes the constrained minmax optimization problems a problem of solving nonlinear equations by a complementarily function. For getting all minmax optimization solutions, the cost function f(x, y) can be constrained as M 1 f(x, y) M 2 by using different real numbers M 1 and M 2. To show effectiveness of the proposed methods, some examples are taken to compare with results in the literature, and it is easy to find that the proposed methods can get all minmax optimization solutions of minmax problems with constraints by using different M 1 and M 2, this implies that the proposed methods has superiority over the methods in the literature (that is based on different initial values to get other minmax optimization solutions).