By Brinkhuis J., Zhang S.
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Extra resources for A D-induced duality and its applications
Oper. Res. 23, 769–805 (1998) 2. : Optimization: insights and applications. Princeton University Press, Princeton (2005) 3. : Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997) 4. : Geometric Algorithms and Combinatorial Optimization. Springer, Heidelberg (1993) 5. : Duality results for conic convex programming. Technical Report 9719/A, Econometric Institute, Erasmus University Rotterdam, The Netherlands (1997) 6. : Multivariate nonnegative quadratic mappings.
It also brings up interesting theoretical questions such as how to characterize the bi-positive cones, and how to compute/approximate the relevant dual objects. A good understanding of this subject appears to be important both for the theory and practice of optimization and for convex analysis in general. As immediate research topics we pose the following two questions: (1) Is it possible to describe using LMI’s the cone (U)∗D where U is a second order cone in X and D is a second order cone in W?
The new type of dual objects is shown to be useful. It also brings up interesting theoretical questions such as how to characterize the bi-positive cones, and how to compute/approximate the relevant dual objects. A good understanding of this subject appears to be important both for the theory and practice of optimization and for convex analysis in general. As immediate research topics we pose the following two questions: (1) Is it possible to describe using LMI’s the cone (U)∗D where U is a second order cone in X and D is a second order cone in W?