‎we consider nonconvex vector optimization problems with variable ordering structures in banach spaces‎. ‎under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

This study aims to deal with a more realistic combined problem of project scheduling and material ordering. The goal is to minimize the total material holding and ordering costs by determining the starting time of activities along with material ordering schedules subject to some constraints. The problem is first mathematically modelled. Then a hybrid simulated annealing and genetic algorithm is...

Cantor conceived set theory in a sequence of six papers published in the Mathematische Annalen during the five year period 1879-1884. In the fifth of these papers, published in 1883, 1 he stated as a law of thought (Denkgesetz) that every set can be well-ordered or, more precisely, that it is always possible to bring any well-defined set into the form of a well-ordered set. Now to call it a law...

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generaliz...

most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. for making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. in line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

Programming languages theory is full of problems that reduce to proving the consistency of a logic, such as the normalization of typed lambda-calculi, the decidability of equality in type theory, equivalence testing of traces in security, etc. Although the principle of transfinite induction is routinely employed by logicians in proving such theorems, it is rarely used by programming languages r...

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational principle for set-valued mappings acting from quasimetric...

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency /minimality. Using advanced tools of variational analysis and generalized differentiation, we esta...

Inconsistency proving of CSPs is typically achieved by a combination of systematic search and arc consistency, which can both be characterized as resolution. However, it is well-known that there are cases where resolution produces exponential contradiction proofs, although proofs of polynomial size exist. For this reason, we will use optimization methods to reduce the proof size globally by 1. ...