Necessary First-Order and Second-Order Optimality Conditions in Discrete-Time Stochastic Systems

Mahmudov N.

Journal of Optimization Theory and Applications, vol.182, no.3, pp.1001-1018, 2019 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 182 Say: 3
  • Nəşr tarixi: 2019
  • Doi nömrəsi: 10.1007/s10957-019-01478-y
  • jurnalın adı: Journal of Optimization Theory and Applications
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.1001-1018
  • Açar sözlər: Discrete-time backward stochastic equations, Discrete-time stochastic systems, Necessary conditions, Stochastic linear quadratic problem
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

In this paper, first-order and second-order necessary conditions for optimality for discrete-time stochastic optimal control problems governed by discrete-time Itô equations are established. A new discrete-time backward stochastic equation and discrete-time backward stochastic matrix equation are introduced. Based on the discrete-time backward stochastic Itô equation, a discrete-time stochastic maximum principle for the stochastic discrete optimal control problems is obtained. Moreover, using the discrete-time backward stochastic matrix equation the second-order necessary conditions for optimality are obtained.