On some geometric conditions for minimality of DCH-functions via DC-duality approach

Kucuk M., TOZKAN D., KÜÇÜK Y.

JOURNAL OF GLOBAL OPTIMIZATION, cilt.69, sa.4, ss.951-965, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s10898-017-0552-7
  • Dergi Adı: JOURNAL OF GLOBAL OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.951-965
  • Anahtar Kelimeler: DC-functions, DCH-functions, Quasidifferential, Minkowski difference, APPROXIMATE SUBDIFFERENTIALS, GENERALIZED DIFFERENTIALS, CONVEX-FUNCTIONS, OPTIMIZATION, CONSTRAINTS
  • Anadolu Üniversitesi Adresli: Evet

Özet

In this study, some optimality conditions for DCH-functions are given in terms of -faces using DC-duality approach. We introduce some geometric characterizations for the solution set of DCH-minimization problems by means of exposed faces and Minkowski difference. Moreover, we prove that given conditions are independent of the choices of representatives of DCH-functions. Also, some of these conditions are employed to find inf-stationary points for a quasidifferentiable optimization problem (QDP), i.e., the directional derivative of the objective function is a DCH-function. Therefore, we present a condition to find stationary points of a QDP. We give some examples to illustrate obtained results.