We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Bárány and Onn with new methods. This is a challenging problem on the borderline of tractability, its complexity is an open question. We perform benchmarking on generic and ill-conditioned problems, as well as recently introduced highly structured problems. We show that some...

A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem. The computation required to solve the feasibility problem depends on the number of monomials used in the decomposition. The Newton polytope is a method to prun...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

• Yair Censor, University of Haifa ([email protected]). A unified approach to physical and equivalent uniform dose constraints in intensity-modulated radiation therapy (IMRT) via the split feasibility problem. Abstract The multiple-sets split feasibility problem requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation ...

In recent decade, development of telecommunications infrastructure has led to rapid exchange of data between the distribution network components and the control center in many developed countries. These changes, considering the numerous benefits of the Distributed Generators (DGs), have made more motivations for distribution companies to utilize these kinds of generators more than ever before. ...

Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and convex quadratic SDP problems to high accuracy successfully. These solvers are based on the augmented Lagrangian method (ALM) applied to the dual problems with...