G. Pataki, "Strong duality in conic linear programming: facial reduction and extended dual", In Computational and Analytical Mathematics (D. Bailey, H. Bauschke, P. Bor- wein, Frank Garvan, M. Th麓era, J. Vanderwerff and H. Wolkowicz eds.), Springer Proceed- ings in Mathematics & ...
continuous-time linear programming problemsstrong duality theorem90C0590C4690C90This note is aimed to correct the strong duality tHsien-Chung WuOptimization: A Journal of Mathematical Programming and Operations ResearchH.-C. Wu, Continuous-Time Linear Programming Problems Revisited: A Perturbation Ap- ...
In fact, you can do a bit better than the strong duality theorem, in terms of coming up with a stopping condition for a linear programming algorithm. You can observe that an optimal solution implies further constraints on the relationship between the primal and the dual problems. In particular...
Theorem 6.12 (Strong Duality Theorem). If both the primal LP and the dual LP have feasible solutions, then they both have optimal solutions, and for any primal optimal solution x and dual optimal solution y we have that cTx=bTy.如果都是最优解,那就「没有中间商赚差价」,消费者最便宜买到的...
Duality for semidefinite programming; Entropy optimization: Interior point methods; Homogeneous selfdual methods for linear programming; Linear programming: Interior point methods; Linear programming: Karmarkar projective algorithm; Matrix completion problems; Potential reduction methods for linear programming; Sem...
Any linear programming problem and its dual can be classified as bounded, unbounded or inconsistent, giving rise to nine possible primal-dual states, which are reduced to six by the weak duality property. Recently, Goberna and Todorov have studied this partition and its stability in continuous ...
Solutions Chapter 5 SECTION 5.1 5.1.4 w w w Throughout this exercise we will use the fact that strong duality holds for convex quadratic problems with linear constraints (cf. Section 3.4). The problem of finding the minimum distance from the origin to a line is written as min 1 2 kxk2...
In this subsection we use linear programming duality and the structure of threshold graphs to provide a linear description of Dn. Lemma 3.3.13 Let S and T be disjoint subsets of {1,…,n}. Then the inequality (3.14)∑i∈Sxi−∑i∈Txi≤|S|(n−1−|T|) is valid for Dn. More...
In Section 3, we first prove that the strong duality between the dual problem and the primal problem holds true under the Slater condition, and then obtain the KKT condition for solving the primal problem. In Section 4, we provide a sufficient condition for guaranteeing the invertibility ...
An alternative approach to the refined duality theory of geometric programming The refined, or strong duality theory of posynomial geometric programming is a comprehensive duality theory which does not depend on the Kuhn-Tucker theore... J Rajgopal - 《Journal of Mathematical Analysis & Applications...