Existence of efficient and properly efficient solutions to problems of constrained vector optimization
From MaRDI portal
Publication:2235148
DOI10.1007/s10107-020-01532-yOpenAlexW3039226795MaRDI QIDQ2235148
Nguyen Van Tuyen, Do Sang Kim, Boris S. Mordukhovich, Tiên Sȯn Phạm
Publication date: 20 October 2021
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.00298
existence theoremspropernessPareto efficient solutionsPalais-Smale conditions\(M\)-tamenessgeoffrion-properly efficient solutions
Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Sensitivity, stability, parametric optimization (90C31) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)
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Cites Work
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- A class of generalized evolution variational inequalities in Banach spaces
- Existence and boundedness of solutions in infinite-dimensional vector optimization problems
- Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone
- The Ekeland variational principle for Henig proper minimizers and super minimizers
- Relative Pareto minimizers for multiobjective problems: Existence and optimality conditions
- Boundedness and nonemptiness of the efficient solution sets in multiobjective optimization
- Theory of multiobjective optimization
- An improved definition of proper efficiency for vector maximization with respect to cones
- Proper efficiency with respect to cones
- Characterizations of the nonemptiness and compactness of solution sets in convex vector optimization
- Ideal, weakly efficient solutions for vector optimization problems
- Existence theorems in vector optimization with generalized order
- On the complexity of testing attainment of the optimal value in nonlinear optimization
- On the existence of Pareto solutions for polynomial vector optimization problems
- Toward effective detection of the bifurcation locus of real polynomial maps
- Detecting bifurcation values at infinity of real polynomials
- Proper efficiency and the theory of vector maximization
- Reaching generalized critical values of a polynomial
- Recession cones and the domination property in vector optimization
- Fixed Point Theory, Variational Analysis, and Optimization
- Genericity in Polynomial Optimization
- Nonconvex minimization problems
- Proper Efficient Points for Maximizations with Respect to Cones
- An Existence Theorem in Vector Optimization
- Variational Analysis
- Coercivity properties and well-posedness in vector optimization
- Variational Analysis and Applications
- On the Existence of Pareto Efficient Points
- Generalized asymptotic functions in nonconvex multiobjective optimization problems
- Set-valued Optimization
