Scalarization approaches are the simplest methods for solving the multiobjective problems. The idea of scalarization is based on decomposition of multiobjective problems into single objective sub-problems. Every one of these sub-problems can be solved in a parallel manner since they are independent with each other. Hence, as a scalarization approach, systematically modification on the desirabil...

We introduce and analyze a novel scalarization technique and an associated algorithm for generating an approximation of the Pareto front (i.e., the efficient set) of nonlinear multiobjective optimization problems. Our approach is applicable to nonconvex problems, in particular to those with disconnected Pareto fronts and disconnected domains (i.e., disconnected feasible sets). We establish the ...

We study spontaneous scalarization in Scalar-Tensor boson stars. We find that scalarization does not occur in stars whose bosons have no self-interaction. We introduce a quartic self-interaction term into the boson Lagrangian and show that when this term is large, scalarization does occur. Strong self-interaction leads to a large value of the compactness (or sensitivity) of the boson star, a ne...

‎a common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎this reformulation is called scalarization approach‎. here, a well-known scalarization approach named pascoletti-serafini scalarization is considered‎. first, some difficulties of this scalarization are discussed and then ...

We study the linear instability and nonlinear dynamical evolution of Reissner-Nordstr\"om (RN) black hole in Einstein-Maxwell-scalar theory asymptotic flat spacetime. focus on coupling function $f(\phi)=e^{-b\phi^2}$ which allows both scalar-free RN solution scalarized solution. first present system parameters during dynamic scalarization. For parameter regions where spontaneous scalarization o...

The aim of this paper is to investigate several inherited properties of convexity for set-valued maps and develop computational procedure based on such inherited properties. In this paper, we introduced two types of characteristic functions by using Tchebyshev scalarization, and defined four types of scalarization functions to characterize the images of set-valued maps.

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133...

This paper presents a new method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the scalar optimization problem constructed by using these functions, enables to compute complete set of weakly efficient, efficient, and properly efficient solutions of multi-objective optim...

Considering a vector optimization problem to which properly efficient solutions are defined by using convex cone-monotone scalarization functions, we attach to it, by means of perturbation theory, new vector duals. When the primal problem, the scalarization function and the perturbation function are particularized, different dual vector problems are obtained, some of them already known in the l...