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Characterizations of ɛ-duality gap statements for constrained optimization problems

100%

Boncea H.-V., Grad S.-M.

Open Mathematics

2013

tom 11

nr 11

2020-2033

In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

100%

Ioan Boţ R., Grad S.-M.

Open Mathematics

2011

tom 9

nr 1

162-172

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when 0 belongs to the range of S + T. Several special cases are discussed, some of them delivering interesting byproducts.

Ograniczanie wyników

2 Open Mathematics

2 Grad S.-M.

1 Boncea H.-V.

1 Ioan Boţ R.

1 2013

1 2011

Wyniki wyszukiwania

Characterizations of ɛ-duality gap statements for constrained optimization problems

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators