Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.Comment: Computational Optimization and Applications, accepted for publicatio

Interactive approaches for biobjective problems with progressively changing solution sets

In this study, we develop interactive approaches to find a satisfactory alternative of a decision maker (DM) having a quasiconvex preference function where the alternative set changes progressively. In this environment, we keep searching the available set of alternatives and estimating the preference function of the DM. As new alternatives emerge, we make better use of the available preference information and eventually converge to a preferred alternative of the DM. We test our approaches on biobjective, multi-item, multi-round auction problems. The results show that our approaches work well in terms of both the preference function value of the obtained solution and the amount of preference information required

On Combining Regression Analysis and Constraint Programming

International audienceUncertain data due to imprecise measurements is commonly specified as bounded interval parameters in a constraint problem. For tractability reasons, existing approaches assume independence of the parameters. This assumption is safe, but can lead to large solution spaces, and a loss of the problem structure. In this paper we propose to combine the strengths of two frameworks to tackle parameter dependency effectively, namely constraint programming and regression analysis. Our methodology is an iterative process. The core intuitive idea is to account for data dependency by solving a set of constraint models such that each model uses data parameter instances that satisfy the dependency constraints. Then we apply a regression between the parameter instances and the corresponding solutions found to yield a possible relationship function. Our findings show that this methodology exploits the strengths of both paradigms effectively, and provides valuable insights to the decision maker by accounting for parameter dependencies

On finding all minimally unsatisfiable subformulas

Abstract. Much attention has been given in recent years to the problem o

On optimal zero-preserving corrections for inconsistent linear systems

Infeasible systems, Nonlinear programming, Fractional programming, Global optimization,