On several concepts for \(\varepsilon\)-efficiency
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Publication:1342424
DOI10.1007/BF01720705zbMath0822.90116MaRDI QIDQ1342424
Siegfried Helbig, Dentcheva, Darinka
Publication date: 11 January 1995
Published in: OR Spektrum (Search for Journal in Brave)
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Exact and approximate vector Ekeland variational principles ⋮ A multiobjective evolutionary algorithm for approximating the efficient set ⋮ On approximate efficiency in multiobjective programming ⋮ On approximate solutions in vector optimization problems via scalarization ⋮ IT-CEMOP: an iterative co-evolutionary algorithm for multiobjective optimization problem with nonlinear constraints ⋮ Metaheuristics and cooperative approaches for the bi-objective ring star problem ⋮ On variational principles, level sets, well-posedness, and \(\epsilon\)-solutions in vector optimization ⋮ Lagrange multiplier rules for weak approximate Pareto solutions to constrained vector optimization problems with variable ordering structures ⋮ Characterizing ϵ-properly efficient solutions ⋮ Equivalent \(\varepsilon\)-efficiency notions in vector optimization ⋮ A generic approach to approximate efficiency and applications to vector optimization with set-valued maps ⋮ Limit sets in global multiobjective optimization ⋮ On a practical notion of Geoffrion proper optimality in multicriteria optimization ⋮ Lagrange multiplier rules for weak approximate Pareto solutions of constrained vector optimization problems in Hilbert spaces ⋮ ∊-Variational inequalities in partially ordered spaces ⋮ Convergence of stochastic search algorithms to finite size Pareto set approximations ⋮ Optimality conditions for metrically consistent approximate solutions in vector optimization ⋮ Cone characterizations of approximate solutions in real vector optimization ⋮ Covers and approximations in multiobjective optimization ⋮ Generalized \(\varepsilon \)-quasi-solutions in multiobjective optimization problems: existence results and optimality conditions ⋮ Stochastic convergence of random search methods to fixed size Pareto front approximations ⋮ On the convergence of multiobjective evolutionary algorithms ⋮ Axiomatic approach to approximate solutions in multiobjective optimization ⋮ Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization ⋮ Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization ⋮ ε-Conjugate maps andε-conjugate duality in vector optimization with set-valued maps ⋮ Approximate proper efficiency for multiobjective optimization problems
Cites Work
- \(\epsilon\)-optimality for bicriteria programs and its application to minimum cost flows
- On two generalizations of Pareto minimality
- Approximation in multiobjective optimization
- Approximate saddle-point theorems in vector optimization
- \(\epsilon\)-duality of nondifferentiable nonconvex multiobjective programming
- Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
- An approximation method for the efficiency set of multiobjective programming problems
- A generalization of ekellandz’s variational principle
- Between Pareto efficiency and Pareto ε-efficiency
- Approximating families of cones and proper efficiency in vector optimization
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