scholarly journals Continuous programming containing arbitrary norms

1985 ◽  
Vol 39 (1) ◽  
pp. 28-38 ◽  
Author(s):  
S. Chandra ◽  
B. D. Craven ◽  
I. Husain
Keyword(s):  
Mathematical Programming ◽  
Constrained Optimization ◽  
Optimality Conditions ◽  
Duality Result ◽  
Duality Results ◽  
Continuous Programming ◽  
Arbitrary Norms ◽  
Abstract Spaces ◽  
Special Case

AbstractOptimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, is deduced as a special case.

scholarly journals On sequential optimality conditions for smooth constrained optimization

Optimization ◽  
2011 ◽  
Vol 60 (5) ◽  
pp. 627-641 ◽  
Author(s):  
Roberto Andreani ◽  
Gabriel Haeser ◽  
J. M. Martínez
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Sequential Optimality Conditions

scholarly journals Sufficient optimality criteria and duality for variational problems with generalised invexity

1989 ◽  
Vol 31 (1) ◽  
pp. 108-121 ◽  
Author(s):  
B. Mond ◽  
I. Husain
Keyword(s):  
Mathematical Programming ◽  
Variational Problems ◽  
Optimality Criteria ◽  
Duality Results

AbstractA number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.

WHY REGULARIZATION OF LAGRANGE PRINCIPLE AND PONTRYAGIN MAXIMUM PRINCIPLE IS NEEDED AND WHAT IT GIVES

2018 ◽  
pp. 757-775
Author(s):  
Mikhail Iosifovich Sumin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Mathematical Programming ◽  
Optimality Conditions ◽  
Pontryagin Maximum Principle ◽  
Lagrange Principle ◽  
Convex Problems ◽  
The Pontryagin Maximum Principle

We consider the regularization of the classical Lagrange principle and the Pontryagin maximum principle in convex problems of mathematical programming and optimal control. On example of the “simplest” problems of constrained infinitedimensional optimization, two main questions are discussed: why is regularization of the classical optimality conditions necessary and what does it give?

scholarly journals Optimality Conditions and Duality for Multiobjective Variational Problems with Generalized -B-Type-I Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
C. Nahak ◽  
N. Behera
Keyword(s):  
Optimality Conditions ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multiobjective Variational Problems ◽  
Generalized Type

We use -type-I and generalized -type-I functions to establish sufficient optimality conditions and duality results for multiobjective variational problems. Some of the related problems are also discussed.

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