We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set...

This article establishes the existence of Lyapunov functions for analyzing stability a class state-constrained systems, and it describes algorithms their numerical computation. The system model consists differential equation coupled with set-valued relation which introduces discontinuities in vector field at boundaries constraint set. In particular, is described by subdifferential indicator fun...

In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdiffer...

In this paper, we investigate new active-settype methods for l1-regularized linear regression that overcome some difficulties of existing active set methods. By showing a relationship between l1-regularized linear regression and the linear complementarity problem with bounds, we present a fast active-set-type method, called block principal pivoting. This method accelerates computation by allowi...

In our earlier work we have developed the axiomatic theory of the scalar cardinality of interval-valued fuzzy sets following Wygralak’s axiomatic theory of scalar cardinalities of fuzzy sets. The cardinality has been defined as a mapping from the set of interval-valued fuzzy sets with finite support to the set of closed subintervals of [0,+∞). We have shown that each scalar cardinality of inter...

In this paper, by using C-class functions, we will present a coupled …xed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. First part of the paper is related to some …xed point theorems, the second part presents the uniqueness and existence for the solution of the coupled …xed point problem and in the third part we...

Most known continuation methods for P 0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and a properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose in this paper a new homotopy formulation for the complementarity problem based on which a new h...

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

We present a fixed time-step algorithm for the simulation of multi-rigid-body dynamics with joints, contact, collision, and friction. The method solves a linear complementarity problem (LCP) at each step. We show that the algorithm can be obtained as the stiff limit of fixed time-step schemes applied to regularized contact models. We do not perform collision detection. Instead, a noninterpenetr...