scholarly journals A new proof of the strong duality theorem for semidefinite programming

2005 ◽  
Vol 303 (2) ◽  
pp. 622-626
Author(s):  
Qingzhi Yang
Keyword(s):  
Semidefinite Programming ◽  
Duality Theorem ◽  
Strong Duality

scholarly journals Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs

2013 ◽  
Vol 9 (3) ◽  
pp. 525-530 ◽  
Author(s):  
Xinmin Yang ◽  
◽  
Jin Yang ◽  
Heung Wing Joseph Lee ◽  
◽  
...  
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Higher Order

scholarly journals Separated and state-constrained separated linear programming problems on time scales

2019 ◽  
Vol 38 (4) ◽  
pp. 181-195 ◽  
Author(s):  
Rasheed Al-Salih ◽  
Martin J. Bohner
Keyword(s):  
Linear Programming ◽  
Time Scales ◽  
Continuous Time ◽  
Duality Theorem ◽  
Strong Duality ◽  
Continuous Time Model ◽  
Time Model ◽  
Wide Range ◽  
Linear Programming Problems ◽  
Fundamental Theorems

Separated linear programming problems can be used to model a wide range of real-world applications such as in communications, manufacturing, transportation, and so on. In this paper, we investigate novel formulations for two classes of these problems using the methodology of time scales. As a special case, we obtain the classical separated continuous-time model and the state-constrained separated continuous-time model. We establish some of the fundamental theorems such as the weak duality theorem and the optimality condition on arbitrary time scales, while the strong duality theorem is presented for isolated time scales. Examples are given to demonstrate our new results

scholarly journals Approximate dual and approximate vector variational inequality for multiobjective optimization

1989 ◽  
Vol 47 (3) ◽  
pp. 418-423 ◽  
Author(s):  
G.–Y. Chen ◽  
B. D. Craven
Keyword(s):  
Variational Inequality ◽  
Multiobjective Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Strong Duality ◽  
Vector Variational Inequality ◽  
Weak Duality ◽  
Multiobjective Optimization Problem ◽  
Feasible Set

AbstractAn approximate dual is proposed for a multiobjective optimization problem. The approximate dual has a finite feasible set, and is constructed without using a perturbation. An approximate weak duality theorem and an approximate strong duality theorem are obtained, and also an approximate variational inequality condition for efficient multiobjective solutions.

A note on strong duality theorem for a multiobjective higher order nondifferentiable symmetric dual programs

OPSEARCH ◽  
2015 ◽  
Vol 53 (1) ◽  
pp. 151-156
Author(s):  
Indira P. Debnath ◽  
S. K. Gupta ◽  
I. Ahmad
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Higher Order

scholarly journals Strong Duality for Semidefinite Programming

1997 ◽  
Vol 7 (3) ◽  
pp. 641-662 ◽  
Author(s):  
Motakuri V. Ramana ◽  
Levent Tunçel ◽  
Henry Wolkowicz
Keyword(s):  
Semidefinite Programming ◽  
Strong Duality

scholarly journals Linear semidefinite programming problems: regularisation and strong dual formulations

2020 ◽  
pp. 17-27
Author(s):  
Olga I. Kostyukova ◽  
Tatiana V. Tchemisova
Keyword(s):  
Semidefinite Programming ◽  
Original Problem ◽  
Equivalent Form ◽  
Strong Duality ◽  
Regularity Conditions ◽  
Index Set ◽  
Duality Property ◽  
Linear Problems ◽  
Implicit And Explicit ◽  
Strong Dual

Regularisation consists in reducing a given optimisation problem to an equivalent form where certain regularity conditions, which guarantee the strong duality, are fulfilled. In this paper, for linear problems of semidefinite programming (SDP), we propose a regularisation procedure which is based on the concept of an immobile index set and its properties. This procedure is described in the form of a finite algorithm which converts any linear semidefinite problem to a form that satisfies the Slater condition. Using the properties of the immobile indices and the described regularization procedure, we obtained new dual SDP problems in implicit and explicit forms. It is proven that for the constructed dual problems and the original problem the strong duality property holds true.

scholarly journals Two types of duality in multiobjective fractional programming

1996 ◽  
Vol 54 (1) ◽  
pp. 99-114 ◽  
Author(s):  
L. Coladas ◽  
Z. Li ◽  
S. Wang
Keyword(s):  
Fractional Programming ◽  
Duality Theorem ◽  
Strong Duality ◽  
Weak Duality ◽  
Multiobjective Fractional Programming ◽  
Dual Problems ◽  
Fractional Program ◽  
Mild Assumption

In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.

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