Outer approximation algorithms for convex vector optimization problems

References

• Ç. Ararat, S. Tekgül, and F. Ulus, Geometric duality results and approximation algorithms for convex vector optimization problems. SIAM Journal on Optimization (to appear), pp. 1–31.
   Google Scholar
• Ç. Ararat, F. Ulus, and M. Umer, A norm minimization-based convex vector optimization algorithm, J. Optim. Theory. Appl. 194 (2) (2022), pp. 681–712.
   Web of Science ®Google Scholar
• T. Bektaş, Disjunctive programming for multiobjective discrete optimisation, INFORMS. J. Comput. 30 (4) (2018), pp. 625–633.
   Web of Science ®Google Scholar
• H.P. Benson, An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem, J. Glob. Optim. 13 (1) (1998), pp. 1–24.
   Web of Science ®Google Scholar
• K. Dächert and K. Klamroth, A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems, J. Glob. Optim. 61 (4) (2015), pp. 643–676.
   Web of Science ®Google Scholar
• D. Dörfler, A. Löhne, C. Schneider, and B. Weißing, A Benson-type algorithm for bounded convex vector optimization problems with vertex selection, Optim. Methods Softw. 37(3) (2022), pp. 1006–1026.
   Web of Science ®Google Scholar
• M. Ehrgott, L. Shao, and A. Schöbel, An approximation algorithm for convex multi-objective programming problems, J. Glob. Optim. 50(3) (2011), pp. 397–416.
   Web of Science ®Google Scholar
• S. Gass and T. Saaty, The computational algorithm for the parametric objective function, Nav. Res. Logist. Q. 2(1-2) (1955), pp. 39–45.
   Google Scholar
• M. Grant and S. Boyd, Graph implementations for nonsmooth convex programs, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Lecture Notes in Control and Information Sciences, Springer-Verlag Limited, 2008, pp. 95–110.
   Google Scholar
• M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, March 2014. Available at http://cvxr.com/cvx.
   Google Scholar
• A. Hamel, B. Rudloff, and M. Yankova, Set-valued average value at risk and its computation, Math. Financ. Econ. 7(2) (2013), pp. 229–246.
   Web of Science ®Google Scholar
• T. Holzmann and J.C. Smith, Solving discrete multi-objective optimization problems using modified augmented weighted Thebychev scalarizations, Eur. J. Oper. Res. 271 (2) (2018), pp. 436–449.
   Web of Science ®Google Scholar
• J. Jahn, Vector Optimization–Theory, Applications, and Extensions, Springer, 2004.
   Google Scholar
• K. Klamroth, J. Tind, and M.M. Wiecek, Unbiased approximation in multicriteria optimization, Math. Methods Oper. Res. 56 (3) (2003), pp. 413–437.
   Web of Science ®Google Scholar
• A. Löhne, Vector Optimization with Infimum and Supremum, Springer, 2011.
   Google Scholar
• A. Löhne and B. Weißing, BENSOLVE: A Free VLP Solver, Version 2.0.1, 2015. Available at https://bensolve.org/.
   Google Scholar
• A. Löhne and B. Weißing, The vector linear program solver bensolve–notes on theoretical background, Eur. J. Oper. Res. 260(3) (2017), pp. 807–813.
   Web of Science ®Google Scholar
• A. Löhne, B. Rudloff, and F. Ulus, Primal and dual approximation algorithms for convex vector optimization problems, J. Glob. Optim. 60(4) (2014), pp. 713–736.
   Web of Science ®Google Scholar
• D. Luc, Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 319, Springer Verlag, 1989.
   Google Scholar
• A. Pascoletti and P. Serafini, Scalarizing vector optimization problems, J. Optim. Theory. Appl. 42(4) (1984), pp. 499–524.
   Web of Science ®Google Scholar
• R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
   Google Scholar
• B. Rudloff and F. Ulus, Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization, Math. Financ. Econ. 15(2) (2021), pp. 397–430.
   Web of Science ®Google Scholar
• J.F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw. 11 (1-4) (1999), pp. 625–653.
   Web of Science ®Google Scholar
• E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evol. Comput. 3(4) (1999), pp. 257–271.
   Web of Science ®Google Scholar