In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

In this paper we introduce a new lattice problem, the subspace avoiding problem (Sap). We describe a probabilistic single exponential time algorithm for Sap for arbitrary `p norms. We also describe polynomial time reductions for four classical problems from the geometry of numbers, the shortest vector problem (Svp), the closest vector problem (Cvp), the successive minima problem (Smp), and the ...

BAN estimators generally admit first order representations which insure them to be also asymptotically Pitman closest. For AN estimators admitting a first order representation, an ordering under the Pitman closeness measure is established and is shown to be isomorphic to the one under 'the usual quadratic norm. Multiparameter problems are also treated in the same vein.

structural repetitive subsequences are most important portion of biological sequences, which play crucial roles on corresponding sequence’s fold and functionality. biggest class of the repetitive subsequences is “transposable elements” which has its own sub-classes upon contexts’ structures. many researches have been performed to criticality determine the structure and function of repetitive su...

We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in the Euclidean norm. We recall the three main families of algorithms for these problems, namely the algorithm by Micciancio and Voulgaris based on the Voronoi cell [STOC’10], the Monte-Carlo algorithms derived from the Ajtai, Kumar and Sivakumar algorithm [STOC’01] and the enumeration algorithms origin...

The Super-SAT (SSAT) problem was introduced in [1], [2] to prove the NP-hardness of approximation two popular lattice problems - Shortest Vector Problem and Closest Problem. SSAT is conjectured be NP-hard approximate within a factor nc (c positive constant, n size instance). In this paper we conjecture assuming Projection Games Conjecture (PGC) [3]. This implies hardness these polynomial factor...

We prove a connection of the worst-case complexity and the average-case complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an eecient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least with a non-trivial success probability over this distribution, we show that one can approximately solve se...