Existence of saddle point of Lagrange function for some classes of mathematical programming problems

Cybernetics ◽  
1982 ◽  
Vol 18 (1) ◽  
pp. 116-122
Author(s):  
V. B. Vilkov ◽  
L. K. Surovtsov
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Lagrange Function ◽  
Mathematical Programming Problems

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.

Computerized Selection of Optimum Machining Conditions for a Job Requiring Multiple Operations

1978 ◽  
Vol 100 (3) ◽  
pp. 356-362 ◽  
Author(s):  
S. S. Rao ◽  
S. K. Hati
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Machine Tools ◽  
Machining Conditions ◽  
Coupling Constraints ◽  
Programming Techniques ◽  
Mathematical Programming Problems ◽  
The Individual ◽  
The Cost ◽  
Selection Of

The problem of determining the optimum machining conditions for a job requiring multiple operations has been investigated. Three objectives, namely, the minimization of the cost of production per piece, the maximization of the production rate and, the maximization of the profit are considered in this work. In addition to the usual constraints that arise from the individual machine tools, some coupling constraints have been included in the formulation. The problems are formulated as standard mathematical programming problems, and nonlinear programming techniques are used to solve the problems.

Sign in / Sign up

Export Citation Format

Share Document