We consider general, typically nonconvex, Quadratic Programming Problems. The Semi-deenite relaxation proposed by Shor provides bounds on the optimal solution, but it does not always provide suuciently strong bounds if linear constraints are also involved. To get rid of the linear side-constraints, another, stronger convex relaxation is derived. This relaxation uses copositive matrices. Special...

Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to generate bounds for mixed-integer linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to strengthen a linear programming relaxation. ...

Nonconvex quadratic constraints can be linearized to obtain relaxations in a wellunderstood manner. We propose to tighten the relaxation by using second order cone constraints, resulting in a convex quadratic relaxation. Our quadratic approximation to the bilinear term is compared to the linear McCormick bounds. The second order cone constraints are based on linear combinations of pairs of vari...

A new relaxation mechanism is shown to arise from overdamped two-level systems above a critical temperature T ∗ ≈ 5 K, thus yielding an explanation for experimental observations in dielectric glasses in the temperature range between T ∗ and the relaxation peak at 50 K. Using the distribution function of the tunnelling model for the parameters of the two-level systems, both the linear decrease o...

The present series of three consecutive papers develops a general theory for linear and fmite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isotherma...

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solvi...

In this paper, three preconditioned parallel multisplitting methods are established for solving the large sparse linear systems, including local preconditioned parallel multisplitting relaxation method, global preconditioned parallel multisplitting relaxation method and global preconditioned nonstationary parallel multisplitting relaxation method. The convergence and comparison results of the m...

This paper considers a single-machine scheduling problem where the decision authorities and information are distributed in multiple sub-production systems. Sub-production systems share the single-machine and must cooperate with each other to achieve a global goal of minimizing a linear function of the completion times of the jobs; e.g., total weighted completion times. It is assumed that neithe...

This paper gives the comparison of some iterative methods (Jacobi method, Gauss–Seidel method and the Successive over-relaxation method) for solving systems of linear equations with their asynchronous implementations. Experiments show the effectiveness of asynchronous iterative methods for solving linear algebra problems on parallel multiprocessor systems.

purpose :   this study was designed to compare the effects of two different relaxation techniques, namely progressive muscle relaxation (pmr) and autogenic relaxation (agr) on moods of young soccer players . methods :   sixteen adolescent athletes (mean age: 14.1 ± 1.3) received either pmr or agr training. using profile of mood states-adolescents, their mood states were measured one week before...