On unconstrained optimization problems solved using the canonical duality and triality theories

Zălinescu, Constantin

doi:10.1080/02331934.2019.1672072

Cited by 3 publications

(2 citation statements)

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“…in general T J+ Q and T J+ Q,col are not convex, unlike their corresponding sets Y + , Y + col and S + , S + col from [18] and [19], respectively. However, taking into account Remark 4, T col , T J+ Q and T J+ Q,col are convex whenever Q 0 = 1, m. In the present context it is natural (in fact necessary) to take λ ∈ Γ Q 0 .…”

Section: Introductionmentioning

confidence: 98%

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On Constrained Optimization Problems Solved Using the Canonical Duality Theory

Zălinescu

2019

Advances in Intelligent Systems and Computing

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DY Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not convincing proofs, or even false results. It is our aim in this work to study rigorously these class of constrained optimization problems in finite dimensional spaces and to discuss several results published in the last ten years. PreliminariesWe consider the following minimization problem with equality and inequality constraintsx ∈ R n , j ∈ 1, m , q k and Λ k being quadratic functions on R n , and V k ∈ Γ sc := Γ sc (R) for k ∈ 0, m; note that X J∪K = X J ∩ X K ∀J, K ⊂ 1, m.(1)

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Section: Introductionmentioning

confidence: 98%

“…However, taking into account Remark 4, T col , T J+ Q and T J+ Q,col are convex whenever Q 0 = 1, m. In the present context it is natural (in fact necessary) to take λ ∈ Γ Q 0 . As in [18] and [19], we consider the (dual objective) function…”

Section: Introductionmentioning

confidence: 99%