Linear and combinatorial sharing problems

Combinatorial problems in solving linear systems

Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today’s numerical linear algebra computations consists of the solution of...

Expressing Combinatorial Optimization Problems by Linear Programs

Many combinatorial optimization problems call for the optimization of a linear function over a certain polytope. Typically, these polytopes have an exponential number of facets. W e explore the problem of finding small l inear programming formulations when one may use any new variables and constraints. W e show that expressing the matching and the Traveling Salesman Problem by a symmetric linea...

Linear, Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems

Linear Complementarity as a General Solution Method to Combinatorial Problems

T paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons ar...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.