Minty Variational Inequalities (for short, MVI) have proved to characterize a kind of equilibrium more qualified than Stampacchia Variational Inequalities (for short, SVI). This conclusion leads to argue that, when a MVI admits a solution and the operator F admits a primitive minimization problem (that is the function f to minimize is such that F = f ′), then f has some regularity property, e.g...

An infinite sequence of 0’s and 1’s evolves by flipping each 1 to a 0 exponentially at rate one. When a 1 flips, all bits to its right also flip. Starting from any configuration with finitely many 1’s to the left of the origin, we show that the leftmost 1 moves right with linear speed. Upper and lower bounds are given on the speed.

We consider two generalized Minty vector variational-like inequalities and investigate the relations between their solutions and vector optimization problems for non-differentiable α-invex functions.

<p style='text-indent:20px;'>This paper deals with the weak versions of vector variational-like inequalities, namely Stampacchia and Minty type under invexity in framework convexificators. The connection between both problems along link to optimization problem are analyzed. An application nonconvex mathematical programming has also been presented. Further, bi-level version these is formul...

Correspondence: [email protected] Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, P. R China Abstract In this article, we prove the existence of solutions for the general variational inequality j(x, y) ≥ f(x) f(y) and Minty type theorem by using the generalized KKM theorem in topological spaces without linear structure. Some properties of solutions set for t...

By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geo...

We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes 16] and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus ...

By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geo...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...