Bounds for the solution set of linear complementarity problems

AbstractWe give here bounds for the feasible domain and the solution norm of Linear Complementarity Problems (LCP). These bounds are motivated by formulating the LCP as a global quadratic optimization problem and are characterized by the eigenstructure of the corresponding matrix. We prove boundedness of the feasible domain when the quadratic problem is concave, and give easily computable bounds for the solution norm for the convex case. We also obtain lower and upper bounds for the solution norm of the general nonconvex problem

Asynchronous Teams for probe selection problems

AbstractThe selection of probe sets for hybridization experiments directly affects the efficiency and cost of the analysis. We propose the application of the Asynchronous Team (A-Team) technique to determine near-optimal probe sets. An A-Team is comprised of several different heuristic algorithms that communicate with each other via shared memories. The A-Team method has been applied successfully to several problems including the Set Covering Problem, the Traveling Salesman Problem, and the Point-to-Point Connection Problem, and lends itself well to the Probe Selection Problem. We designed and developed a C + + program to run instances of the Minimum Cost Probe Set and Maximum Distinguishing Probe Set problems. A program description and our results are presented in the paper

Generalized convexities and generalized gradients based on algebraic operations

AbstractIn this paper, we investigate properties of generalized convexities based on algebraic operations introduced by Ben Tal [A. Ben Tal, On generalized means and generalized convex functions, J. Optim. Theory Appl. 21 (1977) 1–13] and relations between these generalized convexities and generalized monotonicities. We also discuss the (h,φ)-generalized directional derivative and gradient, and explore the relation between this gradient and the Clarke generalized gradient. Definitions of some generalized averages of the values of a generalized convex function at n equally spaced points based on the algebraic operations are also presented and corresponding results are obtained. Finally, the (φ,γ)-convexity is defined and some properties of (φ,γ)-convex functions are derived