On multiple objective programming problems with set functions
49
TL;DR: In this article, the convexity of a subset of a σ-algebra is defined and a Farkas-Minkowski theorem for set functions is proved.
read more
About: This article is published in Journal of Mathematical Analysis and Applications. The article was published on 01 Feb 1985. and is currently open access. The article focuses on the topics: Active set method & Fractional programming.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions
Rita Pini,Chanchal Singh +1 more
TL;DR: In this article, the authors present information on certain generalizations of convexity and their applications to duality theory and optimality conditions, and the purpose of this contribution is to gather information on the generalizations and their application in duality theories.
86
Oil minmax programming problems containing n-set functions
TL;DR: In this paper, the generalized convexity is defined by use of sublinear functionals which satisfy certain convexness-type conditions, such as sufficient optimality conditions and several duality results of Zalmai [24].
39
Optimality conditions and duality for multiobjective measurable subset selection problems
TL;DR: Optimality conditions and several duality results are established under convexity and generalized ρ-convexity assumptions for constrained multiobjective measurable subset selection problems as discussed by the authors, where the objective is to find a subset that minimizes the number of elements in a set.
33
Epigraphs of convex set functions
TL;DR: In this paper, the authors characterized a convex set function by its epigraph and derived a Fenchel duality theorem for set functions with a functional in L∞ and showed that the w∗-closure of such a functional is convex functional.
33
Moreau-Rockafellar Type Theorem for Convex Set Functions*
Hang-Chin Lai,Lai-Jiu Lin +1 more
TL;DR: In this article, the Kuhn-Tucker type condition for an optimal solution of convex programming problem with set functions and the Fritz John type condition of vector-valued minimization problem for set functions are obtained.
32
References
Mathematical Methods and Theory in Games, Programming, and Economics.
S. Vajda,Samuel Karlin +1 more
- 01 Jan 1960
675
Duality in mathematical programming of set functions: On Fenchel duality theorem
TL;DR: In this paper, the generalized Fenchel theorem was proved for the optimization problem of a set function defined on a family of measurable subsets in an atomless finite measure space (X, a, m).
38
Saddle point and duality in the optimization theory of convex set functions
Hang-Chin Lai,Shu-Shih Yang +1 more
TL;DR: In this article, it is proved that a minimization problem of a set function G has an optimal solution if and only if the Lagrangian on X L,(X, ©, m) has a saddle point (Qo, f0) such that G(Q0) = inf GQ(Q), = inf L(Q;f0) where /0 is an element of the conjugate set ©* (for the definition, see the later context).
37