Title: On Duality Theory Related to Approximate Solutions of Vector-Valued Optimization Problems
Abstract: The notion of approximate solutions or ε-solutions emerged early in the development of modern convex analysis. An analogue of the well-known statement concerning the minimum of a convex function and its subgradient also holds in the approximate case: a convex function f has an ε-approximate minimum at x if and only if 0 ∈ ∂ 0 f(x), where ∂ 0 f (x) is the ε-subdifferential of f at x. Particular attention has been paid to ε-subdifferentials (see Hiriart-Urruty, 1982; Demyanov, 1981). This has resulted in the construction of a new class of optimization procedures, the ε-subgradient methods. The virtually complete set of calculation rules derived for the ε-subdifferential has made possible the study and characterization of constrained convex optimization problems in both the real-valued and vector-valued cases, as in Strodiot et al. (1983), or for ordered vector spaces (Kutateladze, 1978).
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 5
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