Computing All Nonsingular Solutions of Cyclic-n Polynomial Using Polyhedral Homotopy Continuation Methods

All isolated solutions of the cyclic-n polynomial equations are not known for larger dimensions than 11. We exploit two types of symmetric structures in the cyclic-n polynomial to compute all isolated nonsingular solutions of the equations efficiently by the polyhedral homotopy continuation method and to verify the correctness of the generated approximate solutions. Numerical results … Read more

Solving Stability Problems on a Superclass of Interval Graphs

We introduce a graph invariant, called thinness, and show that a maximum weighted stable set on a graph $G(V, E)$ with thinness $k$ may be found in $O(\frac{|V|}{k})^k$-time, if a certain representation is given. We show that a graph has thinness 1 if and only if it is an interval graph, while a graph with … Read more

Optimality Conditions for Vector Optimization with Set-Valued Maps

Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary … Read more

Constructing Approximations to the Efficient Set of Convex Quadratic Multiobjective Problems

In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point … Read more

An explicit equivalent positive semidefinite program for nonlinear 0-1 programs

We consider the general nonlinear optimization problem in 0-1 variables and provide an explicit equivalent positive semidefinite program in $2^n-1$ variables. The optimal values of both problems are identical. From every optimal solution of the former one easily find an optimal solution of the latter and conversely, from every solution of the latter one may … Read more

Dynamic Weighted Aggregation for Evolutionary Multiobjective Optimization

Weighted sum based approaches to multiobjective optimization is computationally very efficient. However,they have two main weakness: 1) Only one Pareto solution can be obtained in one run 2) The solutions in the concave part of the Pareto front cannot be obtained. This paper proposes a new theory on multiobjective optimization using weighted aggregation approach. Based … Read more

Near-optimal solutions to large scale facility location problems

We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x … Read more

Generalized Goal Programming: Polynomial Methods and Applications

In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, … Read more

On implementing a primal-dual interior-point method for conic quadratic optimization

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 … Read more

Cooperative games on antimatroids

The aim of this paper is to introduce cooperative games with a feasible coalition system which is an antimatroid. These combinatorial structures generalize the permission structures, which have nice economical applications. With this goal, we first characterize the approaches from a permission structure with special classes of antimatroids. Next, we use the concept of interior … Read more