The minimum hub cover is a new NP-hard optimization problem that has been recently introduced to the literature in the context of graph query processing. Although a standard set covering formulation has been given, alternate models have not been studied before. This paper fills in that gap and proposes several new mathematical programming models. We give two binary integer programming formulati...

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative appr...

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can ...

In this paper, we study trilinear optimization problems with nonconvex constraints under some assumptions. We first consider the semidefinite relaxation (SDR) of the original problem. Then motivated by So [3], we reduce the problem to that of determining the L2-diameters of certain convex bodies, which can be approximately solved in deterministic polynomial-time. After the relaxed problem being...

We consider nonconvex quadratic optimization problems with binary constraints. Our main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in terms of the problem’s data. We also study the relations between optimal solutions of the nonconvex ...

Solving large scale optimization problems requires a huge amount of computational power. The size of optimization problems that can be solved on a few CPUs has been limited due to a lack of computational power. Grid and cluster computing has received much attention as a powerful and inexpensive way of solving large scale optimization problems that an existing single-unit CPU cannot process. The...

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a quadratically constrained quadratic program (QCQP), a quadratic program with complementarity constraints (QPCC), and rank con...

We consider multi-target linear-quadratic control problem on semiinfinite interval. We show that the problem can be reduced to a simple convex optimization problem on the simplex

Solving large scale optimization problems requires a huge amount of computational power. The size of optimization problems that can be solved on a few CPUs has been limited due to a lack of computational power. Grid and cluster computing has received much attention as a powerful and inexpensive way of solving large scale optimization problems that an existing single CPU cannot process. The aim ...

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization pointof-view. Rather than trying to compute the global minimum a goal we consider as elusive in these cases we wish to design opt...