A refinement of the concept of equilibrium in multiple objective continous games.
We present a regularization method to approach a solution of the pessimistic formulation of ill-posed bilevel problems. This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.
We study polyconvex envelopes of a class of functions related to the function of Kohn and Strang introduced in . We present an example of a function of this class for which the polyconvex envelope may be computed explicitly and we also point out some general features of the problem.
Ant Colony Optimization (ACO) is a recent metaheuristic method that is inspired by the behavior of real ant colonies. In this paper, we review the underlying ideas of this approach that lead from the biological inspiration to the ACO metaheuristic, which gives a set of rules of how to apply ACO algorithms to challenging combinatorial problems. We present some of the algorithms that were developed under this framework, give an overview of current applications, and analyze the relationship between...
A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear...
In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency...
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...