Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...

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A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obt...

In the current work, we have formulated the optimal bit-allocation problem for a scalable codec of images or videos as a constrained vector-valued optimization problem and demonstrated that there can be many optimal solutions, called Pareto optimal points. In practice, the Pareto points are derived via the weighted sum scalarization approach. An important question which arises is whether all th...

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In slow rotation approximation $a\ll1$ with parameter $a$, GB term is given by a for Schwarzschild hole, whereas CS takes linear $a$. The tachyonic instability represents onset spontaneous scalarization. use (2+1)-dimensional hyperboloidal foliation method to show considering...

We define the quasi-minimal elements of a set with respect to a convex cone and characterize them via linear scalarization. Then we attach to a general vector optimization problem a dual vector optimization problem with respect to quasi-efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem we derive vector dual problems ...

In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.[1], from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexa...

Marcelo Salgado, Daniel Sudarsky Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Apdo. Postal 70-543 México 04510 D.F, México and Ulises Nucamendi Departamento de F́ısica Centro de Investigación y de Estudios Avanzados del I.P.N. A. P. 14-741, México, D. F. 07000, México. Abstract We study in the physical frame the phenomenon of spontaneous scalarization that occurs in sc...

This is an overview of a few possibilities that are open by model theory in applied mathematics. The most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. DOI: 10.1134/S1990478909010116 The union of functional analys...