scholarly journals Optimality Conditions and Generalized Gradient Methods for Mathematical Programming Problems Including Extremal-Value Functions

1985 ◽  
Vol 21 (8) ◽  
pp. 778-785
Author(s):  
Kiyotaka SHIMIZU ◽  
Yo ISHIZUKA ◽  
Hirohisa OTA
Keyword(s):  
Mathematical Programming ◽  
Optimality Conditions ◽  
Gradient Methods ◽  
Value Functions ◽  
Generalized Gradient ◽  
Mathematical Programming Problems ◽  
Extremal Value

scholarly journals Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

2019 ◽  
Vol 29 (4) ◽  
pp. 433-448
Author(s):  
Kunwar Singh ◽  
J.K. Maurya ◽  
S.K. Mishra
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Dual Model ◽  
Equilibrium Constraints ◽  
Convexity Assumptions ◽  
Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

scholarly journals Error Bound property in mathematical programming

2019 ◽  
Vol 55 (3) ◽  
pp. 309-318
Author(s):  
D. E. Berezhnov ◽  
L. I. Minchenko
Keyword(s):  
Mathematical Programming ◽  
Large Class ◽  
Optimality Conditions ◽  
Error Bound ◽  
Numerical Optimization ◽  
Constraint Qualification ◽  
Necessary Conditions ◽  
Optimization Algorithms ◽  
Sufficient Conditions ◽  
Mathematical Programming Problems

This article is devoted to the Error Bound property (also named R-regularity) in mathematical programming problems. This property plays an important role in analyzing the convergence of numerical optimization algorithms, a topic covered by multiple publications, and at the same time it is a relatively generic constraint qualification that guarantees the satisfaction of the necessary Kuhn – Tucker optimality conditions in mathematical programming problems. In the article, new sufficient conditions for the error bound property are described, and it’s also shown that several known necessary conditions are insufficient. The sufficient conditions obtained can be used to prove the regularity of a large class of sets including sets that cannot be proven regular by other known constraints.

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