Circular meshes are quadrilateral meshes all of whose faces possess a circumcircle,whereas conicalmeshes areplanar quadrilateralmeshes where the faces which meet in a vertex are tangent to a right circular cone. Both are amenable to geometricmodeling – recently surface approximation and subdivision-like refinement processes have been studied. In this paper we extend the original defining proper...

Abstract In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) preordered by a not necessarily solid (and pointed) convex cone. It well-known that there are many examples ordering cone has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim consider Pareto-type solu...

In this paper, we consider a vector optimization problem over cones involving support functions in objective as well as constraints and associate a unified higher order dual to it. Duality result have been established under the conditions of higher order cone convex and related functions. A number of previously studied problems appear as special cases.

in this study, a bearing capacity device is designed and fabricated to determine the load-settlement behavior of three circular footing models resting above the ground water table. capillary rise in the studied well graded sand is measured and the level of the water table is controlled at the desired heights during each bearing capacity test. moreover, shear strength parameters and soil water r...

In this work, we propose a proximal algorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programm...

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 ...

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...

A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum(-line...

We consider two notions for the representations of convex cones: G-representation and liftedG-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one noti...

In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdiffer...