In the presence of certain non-minimal couplings between a scalar field and Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long they are spinning fast enough. This provides distinctive violation hypothesis, occurring only for some high spin range. this paper we assess if strong magnetic fields, that may exist in vicinity astrophysical holes, could facilitate effect, by bri...

Abstract We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used deal problem. Here, we utilize concept frontier map that extends notion optimal value function our parametric Based on this, build t...

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of rotating in the Einstein-scalar-Chern-Simons (EsCS) theory. In slow rotation approximation, CS term takes a linear form parameter $a$ which determines tachyonic instability. The instability for represents onset spontaneous scalarization. shown unstable against spherically symmetric sca...

It is well known that equilibrium problems are very important mathematical models and are closely related with fixed point problems, variational inequalities, and Nash equilibrium problems. Gap functions and error bounds which play a vital role in algorithms design, are two much-addressed topics of vector equilibrium problems. This paper is devoted to studying the scalar-valued gap functions an...

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of all Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions corresponding to one Pareto efficient/Henig proper efficient/super effic...

Optimization is an important tool in computational finance and business intelligence. Multiple criteria mathematical program(MCMP), which is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously, is one of the ways of utilizing optimization techniques. Due to the existence of multiple objectives, MCMPs are usually difficult t...

We consider scalarization issues for vector problems in the case where the preference relation is represented by a rather arbitrary set. An algorithm for weights choice for a priori unknown preference relations is suggested. Some examples of applications to vector optimization, game equilibrium, and variational inequalities are described. DOI: 10.3103/S1066369X12090022

In a stochastic and fuzzy environment, a multi-objective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and scalarization functions respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using λ-optimal stopping times.

In this paper by using the scalarization method, we consider Stamppachia variational-like inequalities in terms of normal subdifferential for set-valued maps and study their relations with set-valued optimization problems. Furthermore, some characterizations of the solution sets of K-pseudoinvex extremum problems are given.