This paper presents a Branch and Bound method for a nonconvex integer quadratic programming problem with a separable objective function over a bounded box. For this problem, a special branch method is constructed, which has a property that if a box has been partitioned into 2 sub-boxes, then at least one sub-box can be deleted. We analyze the complexity of the algorithm, and prove that it is be...

We consider the entanglement marginal problem, which consists of deciding whether a number reduced density matrices are compatible with an overall separable quantum state. To tackle this we propose hierarchies semidefinite programming relaxations set state marginals admitting fully extension. connect completeness each hierarchy to resolution analog classical problem and thus identify relevant e...

Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.

A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally pr...

Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

  The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...

This paper discusses an Interval Quadratic Programming (IQP) problem, where the constraints coefficients and the right-hand sides are represented by interval data. First, the focus is on a common method for solving Interval Linear Programming problem. Then the idea is extended to the IQP problem. Based on this method each IQP problem is reduced to two classical Quadratic Programming (QP) proble...

For a large-scale quadratic programming problem with separable objective function, a variant of the conjugate gradient method can effectively be applied to the dual problem. In this paper, we consider a block-parallel modification of the conjugate gradient method, which is suitable for implementation on a parallel computer. More precisely, the method proceeds in a block Jacobi manner and execut...