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Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

Stasiak A.

Journal of Applied Analysis

2018

Vol. 24, nr 1

45--54

Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212-221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Higher-order conditions for local equilibria in a discontinuous Gale economic model

Michalak A., Studniarski M.

Control and Cybernetics

2017

Vol. 46, no. 1

37--47

The paper introduces the concept of a strict local equilibrium of order k in the Gale economic model. We obtain higher-order necessary and suﬃcient conditions for such equilibria without assuming continuity of the utility functions. These conditions are formulated in terms of generalized lower and upper directional derivatives, introduced by Studniarski (1986). A stability theorem for strict local equilibria of order k is also included.

Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model

Michalak A., Studniarski M.

Opuscula Mathematica

2014

Vol. 34, no. 4

827--835

In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.