Robust vector optimization with a variable domination structure

2017 ◽  
Vol 33 (3) ◽  
pp. 343-351
Author(s):  
ELISABETH KOBIS ◽  
◽  
CHRISTIANE TAMMER ◽  
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Robust Solutions ◽  
Definition Of ◽  
Vector Valued

In this paper we propose a new definition of robustness for uncertain vector-valued optimization problems equipped with a variable domination structure, derive scalarization results and present algorithms for computing robust solutions.

scholarly journals Vector variational-like inequalities and vector optimization problems

2014 ◽  
Vol 30 (1) ◽  
pp. 101-108
Author(s):  
MIHAELA MIHOLCA ◽  
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Vector Optimization Problems ◽  
Limiting Subdifferential ◽  
Generalized Invexity ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Mordukhovich Limiting Subdifferential

In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential.

scholarly journals On V-r-invexity and vector variational-like inequalities

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 1065-1073 ◽  
Author(s):  
S.K. Mishra ◽  
Vivek Laha
Keyword(s):  
Multiobjective Optimization ◽  
Vector Optimization ◽  
Critical Points ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Multiobjective Optimization Problems ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Weak Vector

In this paper, we consider the multiobjective optimization problems involving the differentiable V-r-invex vector valued functions. Under the assumption of V-r-invexity, we use the Stampacchia type vector variational-like inequalities as tool to solve the vector optimization problems. We establish equivalence among the vector critical points, the weak efficient solutions and the solutions of the Stampacchia type weak vector variational-like inequality problems using Gordan?s separation theorem under the V-r-invexity assumptions. These conditions are more general than those appearing in the literature.

scholarly journals To the question of regularization of vector optimization problems

2021 ◽  
Vol 16 ◽  
pp. 99
Author(s):  
P.I. Kogut ◽  
I.V. Nechai
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Lower Semicontinuous ◽  
Sufficient Conditions ◽  
Vector Optimization Problems ◽  
Method Of Regularization ◽  
Vector Valued

We propose the method of regularization of one class of vector optimizations problems in Banach spaces, in case where vector-valued mapping is not lower semicontinuous in certain sense, which implies violation of sufficient conditions of solvability.

The Rise of Partnerships: From Local to Global

2018 ◽  
Author(s):  
Barbara Gray ◽  
Jill Purdy
Keyword(s):  
Nongovernmental Organizations ◽  
Public Services ◽  
Civic Society ◽  
Robust Solutions ◽  
Essential Components ◽  
Critical Issues ◽  
Definition Of ◽  
Societal Problems ◽  
Shared Norms ◽  
Multistakeholder Partnerships

Multistakeholder partnerships (MSPs) are formed to tackle knotty societal problems, promote innovation, provide public services, expand governance capabilities, set standards for a field, or resolve conflicts that impede progress on critical issues. Partnerships are viewed as collaboration among four types of stakeholders: businesses, governments, nongovernmental organizations (NGOs), and civic society. The objective of collaboration is to create a richer, more comprehensive appreciation of the iss/problem than any of the partners could construct alone by viewing it from the perspectives of all the stakeholders and designing robust solutions. Such partnerships are necessary because few organizations contain sufficient knowledge and resources to fully analyze issues and take action on them unilaterally. Five essential components of a rigorous definition of collaboration are presented: interdependence among partners, emergence of shared norms, wrestling with differences, respect for different competencies, and assuming joint responsibility for outcomes. Several examples of MSPs are provided.

scholarly journals Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Qinghai He ◽  
Weili Kong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Value Set ◽  
Set Valued Mapping ◽  
Optimal Value

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

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