Sparsity-preserving sor algorithms for separable quadratic and linear programming

Linear Time Algorithms for Some Separable Quadratic Programming Problems

A large class of separable quadratic programming problems is presented The problems in the class can be solved in linear time The class in cludes the separable convex quadratic transportation problem with a xed number of sources and separable convex quadratic programming with nonnegativity con straints and a xed number of linear equality constraints

Sparsity Preserving Algorithms for Octagons

Known algorithms for manipulating octagons do not preserve their sparsity, leading typically to quadratic or cubic time and space complexities even if no relation among variables is known when they are all bounded. In this paper, we present new algorithms, which use and return octagons represented as weakly closed difference bound matrices, preserve the sparsity of their input and have better p...

Primal-Dual Projected Gradient Algorithms for Extended Linear-Quadratic Programming

Many large-scale problems in dynamic and stochastic optimization can be modeled with extended linear-quadratic programming, which admits penalty terms and treats them through duality. In general the objective functions in such problems are only piecewise smooth and must be minimized or maximized relative to polyhedral sets of high dimensionality. This paper proposes a new class of numerical met...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

Approximation Algorithms for Quadratic Programming

We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m = 1, we rigorously show that an-minimizer, where error 2 (0; 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1==). For m 2, we present a polynomial-time (1 ? 1 m 2)-a...