• Title/Summary/Keyword: saddle-point theorems

Search Result 7, Processing Time 0.022 seconds

ON DUALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

  • Lee, Gue Myung;Kim, Moon Hee
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.26 no.4
    • /
    • pp.723-734
    • /
    • 2013
  • A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH A MODIFIED OBJECTIVE FUNCTION

  • Kim, Do-Sang
    • Communications of the Korean Mathematical Society
    • /
    • v.20 no.4
    • /
    • pp.837-847
    • /
    • 2005
  • We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.

EXISTENCE OF PERIODIC SOLUTIONS WITH PRESCRIBED MINIMAL PERIOD FOR A FOURTH ORDER NONLINEAR DIFFERENCE SYSTEM

  • LIU, XIA;ZHOU, TAO;SHI, HAIPING
    • Journal of applied mathematics & informatics
    • /
    • v.36 no.5_6
    • /
    • pp.491-504
    • /
    • 2018
  • In this article, we consider a fourth order nonlinear difference system. By making use of the critical point theory, we obtain some new existence theorems of at least one periodic solution with minimal period. Our main approach used in this article is the variational technique and the Saddle Point Theorem.