INFIMAL CONVOLUTION AND DUALITY IN CONVEX MATHEMATICAL PROGRAMMING

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Mahmudov E., Mardanov M. J.

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, cilt.48, sa.1, ss.50-62, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.30546/2409-4994.48.1.2022.50
  • Dergi Adı: PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.50-62
  • Anahtar Kelimeler: Conjugate, duality, dual cone, infimal convolution, indicator function, Lagrange function, INTERIOR-POINT ALGORITHMS, DIFFERENTIAL-INCLUSIONS, OPTIMIZATION PROBLEMS, DISCRETE
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

In the paper it is considered a convex programming problem (CPP) with functional and non-functional constraints. In contrast to previous works, in the study of convex optimization problems, we do not deal with the classical approach of perturbations. In particular, thanks to the new representation of the indicator function on a convex set, the successful use of the infimal convolution method in this work plays a key role in proving duality results for problem CPP. Also, we consider a convex mathematical programming problem with inequality and linear equality constraints given by some matrix. In this case, it turns out that the dual cone to the cone of tangent directions coincides with the set of the image of the points of transposed matrix, taken with a minus sign.