G. Pataki. Strong duality in conic linear programming: facial re- duction and extended duals. In David Bailey, Heinz H. Bauschke, Frank Garvan, Michel Thera, Jon D. Vanderwerff, and Henry Wolkowicz, editors, Computational and analytical mathematics, volume 50 of Springer Proc. Math. Stat.,...
The Lagrangian dual of the CDT subproblem is a semidefinite program (SDP), hence convex and solvable. However, a positive duality gap may exist between the CDT subproblem and its Lagrangian dual because the CDT subproblem itself is nonconvex. In this paper, we present a necessary and ...
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...
Remark 2.3 Lemma 2.1 (i) states that the closure of FSS (recall that it is always convex) coincides with the closed convex set F . However, the evenly convex hull of FSS does not Fig. 1 The sets F , FS and FSS asociated to σ in Example 2.2 Duality for Sets of Strong Slater ...
31 Travis Scrimshaw - Limit shapes from skew Howe duality 44:55 Guofang Wei - Spaces with Ricci curvature lower bounds 36:09 Adrian Tanasa - Tensor models 42:51 David Ruelle - Louis Michel et son rôle au sein de l'IHES 16:01 Stéphane Gaubert - The Nullstellensatz and Positivstellen...
Kronecker product of matrices. This follows from Schur–Weyl duality (see Kraft & Procesi 1996). A simple consequence is that g λ µ,ν can be positive only if ℓ(λ) ≤ ℓ(µ)ℓ(ν). Another consequence is provided by the following lemma. Lemma 2.1. Let µ, ν, λ be ...
V.Jeyakumar, G.Y.Li, "Strong Duality in Robust Semi Definite Linear Programming under Data Uncertainty ", March 1, 2012Jeyakumar, V., Li, G. Y. (2012). Strong duality in robust semi- definite linear programming under data uncertainty. Optimization, DOI:10.1080/02331934.2012.690760....
In the case of a spectral norm uncertainty set, it yields a corresponding strong duality result with a semi-definite programming as its dual. We also show that the dual can be reformulated as a second-order cone programming problem or a linear programming problem when the ...
Optimization: A Journal of Mathematical Programming and Operations ResearchV.Jeyakumar, G.Y.Li, "Strong Duality in Robust Semi Definite Linear Programming under Data Uncertainty ", March 1, 2012Jeyakumar, V., Li, G. Y. (2012). Strong duality in robust semi- definite linear programming ...
Just as in linear programming, duality theorem plays a basic and an important role in theory as well as in algorithmics. Based on the discretization method and convergence property, this paper proposes a new proof of the strong duality theorem for semidefinite programming, which is different from...