Mixed type duality for a programming problem containing support function

2004 ◽  
Vol 15 (1-2) ◽  
pp. 211-225 ◽  
Author(s):  
I. Husain ◽  
Z. Jabeen
Keyword(s):  
Programming Problem ◽  
Support Function ◽  
Mixed Type ◽  
Mixed Type Duality

scholarly journals Mixed-type duality for multiobjective fractional variational control problems

2005 ◽  
Vol 2005 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Raman Patel
Keyword(s):  
Nonlinear Programming ◽  
Convex Functions ◽  
Mixed Type ◽  
Efficient Solutions ◽  
Control Problems ◽  
Duality Results ◽  
Finite Dimensional ◽  
Duality Relations ◽  
Mixed Type Duality ◽  
Convexity Assumptions

The concept of mixed-type duality has been extended to the class of multiobjective fractional variational control problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained forρ-convex (generalizedρ-convex) functions. The results generalize a number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions.

scholarly journals A method of redundant constraint elimination in the problem of body recovery based on support function measurements

2015 ◽  
pp. 348-359
Author(s):  
И.А. Палачев
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Support Function ◽  
New Method ◽  
Quadratic Programming Problem ◽  
New Approach ◽  
Recovery Algorithm ◽  
Redundant Constraint ◽  
Order Of Magnitude ◽  
Recovery Methods

Предложен новый алгоритм восстановления тел по измерениям их опорных функций, который представляет собой алгоритм квадратичного или линейного программирования в форме Гарднера-Кидерлена с меньшим числом ограничений. Уменьшение числа ограничений достигается за счет нового метода, который позволяет исключить из исходной системы ограничений часть ограничений как избыточные. Предложен новый подход, позволяющий применять методы восстановления тел по измерениям опорной функции к задаче восстановления тел по теневым контурам. Представлено описание реализации алгоритма, а также результаты его тестирования на реальных промышленных теневых контурах. Предложенный метод в рассмотренном примере позволил сократить число ограничений на 80% и ускорить исходный алгоритм Гарднера-Кидерлена на порядок. A new body recovery algorithm based on support function measurements is proposed. The proposed algorithm represents a linear or quadratic programming problem in Gardner-Kiderlen form with smaller number of constraints. The reduction of constraint number is based on a new method that allows one to eliminate a part of initial constraints as redundant. A new approach of body recovery based on shadow contours is proposed. It allows one to reuse body recovery methods based on support function measurements. The implementation of the algorithm is described and some results of its testing on real industrial contours are discussed. The proposed method ensures the reduction of constraint number by 80% in the discussed example and also enables to speedup the initial Gardner-Kiderlen algorithm by an order of magnitude.

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