We present an affine-invariant approach for solving linear programs. Unlike previous approaches, the potential strong polynomiality of the new approach does not require that graphs of polytopes have polynomial diameter (the Hirsch conjecture or weaker versions). We prove that two natural realizations of the approach work efficiently for deformed products [1], a class of polytopes that generaliz...

We present here results about the existence of periodic orbits for projected dynamical systems (PDS) under Minty-Browder monotonicity conditions. The results are formulated in the general context of a Hilbert space of arbitrary (finite or infinite) dimension. The existence of periodic orbits for such PDS is deduced by means of nonlinear analysis, using a fixed point approach. It is also shown h...

Abstract In this paper, we introduce and investigate a new kind of coupled systems, called variational inequalities, which consist two elliptic mixed inequalities on Banach spaces. Under general assumptions, by employing Kakutani-Ky Fan fixed point theorem combined with Minty technique, prove that the set solutions for inequality (CVI, short) under consideration is nonempty weak compact. Then, ...

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others special cases. This paper presents picture for relationship between points Moreau proximal mapping solutions that satisfies some kinds monotonicity Lipschitz-type condition.