Geometric Duality for Convex Vector Optimization Problems

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This article extends the geometric duality theory to convex vector optimization problems.

[1]  Lizhen Shao,et al.  A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming , 2012, J. Glob. Optim..

[2]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[3]  Birgit Rudloff,et al.  An algorithm for calculating the set of superhedging portfolios in markets with transaction costs , 2011, 1107.5720.

[4]  Alberto Seeger,et al.  Second Derivatives of a Convex Function and of Its Legendre-Fenchel Transformate , 1992, SIAM J. Optim..

[5]  R. Rockafellar.  First- and second-order epi-differentiability in nonlinear programming , 1988 .

[6]  C. Zălinescu.  Convex analysis in general vector spaces , 2002 .

[7]  Andreas Löhne,et al.  Geometric Duality in Multiple Objective Linear Programming , 2008, SIAM J. Optim..

[8]  Jean-Pierre Crouzeix,et al.  A relationship between the second derivatives of a convex function and of its conjugate , 1977, Math. Program..

[9]  A. Hamel.  Translative Sets and Functions and their Applications to Risk Measure Theory and Nonlinear Separation , 2006 .

[10]  Philip D. Plowright,et al.  Convexity , 2019, Optimization for Chemical and Biochemical Engineering.

[11]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[12]  A. Seeger.  Second-order normal vectors to a convex epigraph , 1994, Bulletin of the Australian Mathematical Society.

[13]  J. Hiriart-Urruty,et al.  The Second-Order Subdifferential and the Dupin Indicatrices of a Non-Differentiable Convex Function , 1989 .

[14]  R. T. Rockafellar,et al.  Generalized second derivatives of convex functions and saddle functions , 1990 .

[15]  Andreas Löhne,et al.  Vector Optimization with Infimum and Supremum , 2011, Vector Optimization.