Sufficiency Conditions and a Duality Theory for Mathematical Programming Problems in Arbitrary Linear Spaces

1970 ◽  
pp. 323-348 ◽  
Author(s):  
LUCIEN W. NEUSTADT
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Linear Spaces ◽  
Mathematical Programming Problems ◽  
Sufficiency Conditions

Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints

1979 ◽  
Vol 21 (1) ◽  
pp. 37-44 ◽  
Author(s):  
C. H. Scott ◽  
T. R. Jefferson
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Linear Constraints ◽  
Lagrangian Formalism ◽  
Symmetric Duality ◽  
Mathematical Programs ◽  
Convex Functionals ◽  
Mathematical Programming Problems

AbstractRecently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.

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.

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