where C ⊆ Rm is a closed convex and pointed cone with nonempty interior intC. (WVVI) was firstly introduced by Giannessi []. It has been shown to have many applications in vector optimization problems and traffic equilibrium problems (e.g., [, ]). Error bounds are to depict the distance from a feasible solution to the solution set, and have played an important role not only in sensitivity an...

It is well known that two types of gravitational wave memory exist in general relativity (GR): the linear memory and the non-linear, or Christodoulou memory. These effects, especially the latter, depend on the specific form of Einstein equation. It can then be speculated that in modified theories of gravity, the memory can differ from the GR prediction, and provides novel phenomena to study the...

It has been shown recently that the charged black hole can be scalarized if Maxwell field minimally couples with a complex scalar which nonnegative nonlinear potential. We firstly prove such scalarization cannot result of continuous phase transition for general Furthermore, we numerically find it is possible RN will by first order spontaneously and extreme not stable in micro-canonical ensemble...

Abstract Scalarization is a common technique to transform multiobjective optimization problem into scalar-valued problem. This article deals with the weighted Tchebycheff scalarization applied discrete problems. consists of minimizing maximum distance image feasible solution some desirable reference point. By choosing suitable weight, any Pareto optimal can be obtained. In this article, we prov...

a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X = A+BWC for positive integer s and real t, whereW is a standard normal random vector and A, B, C are appropriately dimensioned constantmatrices.We solve the problems by amatrix product scalarization technique and interpret the solutions in system-theoretic terms. The results...

In this paper, the existence theorems of solutions for generalized weak vector equilibrium problems are developed in real reflexive Banach spaces. Based on recession method and scalarization technique, we derive a characterization of nonemptiness and boundedness of solution set for generalized weak vector equilibrium problems. Moreover, Painlevé-Kuratowski upper convergence of solution set is a...

A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that pro...