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Second-order optimality conditions in nonsmooth vector optimization

Yadav Priyanka

Control and Cybernetics

2023

Vol. 52, No. 1

35--51

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.

Positive solution for nonlinear fractional differential equation with integral boundary value condition

Zatla Y. T., Daudi-Merzagui N.

Fasciculi Mathematici

2018

Nr 61

163--177

In this paper, we consider a fractional differential equation, with integral boundary conditions, when the nonlinearities are sign changing. Our approach is based on the Krasnoselskii theorem in double cones. We generalize some recent results.

On additive correspondences

Aghajani M., Smajdor A.

Journal of Applied Analysis

2015

Vol. 21, nr 1

59--61

The existence of additive selections of additive correspondences was investigated in [3, 4, 6] and other papers. In this article, we find an existence theorem for additive selections of additive correspondences with convex compact values in a real normed linear space defined on an open convex cone of a real separable normed space.

Advances in cone-based preference modeling for decision making with multiple criteria

Wiecek M. M.

Decision Making in Manufacturing and Services

2007

Vol. 1, no. 1-2

153-173

Decision making with multiple criteria requires preferences elicited from the decision maker to determine a solution set. Models of preferences, that follow upon the concept of nondominated solutions introduced by Yu (1974), are presented and compared within a unified framework of cones. Polyhedral and nonpolyhedral, convex and nonconvex, translated, and variable cones are used to model different types of preferences. Common mathematical properties of the preferences are discussed. The impact of using these preferences in decision making is emphasized.

How to recognize cylinders, cones and tangential developables

Opozda B.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 3

317-323

In the paper we introduce affine invariants which allow to give an easy algorithm to find out the shape of a developable surface.