The purpose of this paper is to obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We show that every stable set always contains the core. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its core … Read more
The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into … Read more
We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach … Read more
We consider a Markov decision process model of a network revenue management problem. Working within this formal framework, we study policies that combine aspects of mathematical programming approaches and pure Markov decision process methods. The policies employ heuristics early in the booking horizon, and switch to a more-detailed decision rule closer to the time of … Read more
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
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
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
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
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
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