An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems
Published Online:1 Nov 2006https://doi.org/10.1287/moor.1060.0221
References
- . Towards finding global representations of the efficient set in multiple objective mathematical programming. Naval Res. Logist. (1997) 44:47–67Crossref, Google Scholar
- Complementarity and interior point methodology. (1995) . Master’s thesis, Department of Statistics, Probability and Operations Research, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, The NetherlandsGoogle Scholar
- . An interior-point approach to parametric convex quadratic programming. (1996) . Working paper, Erasmus University Rotterdam, Rotterdam, The Netherlands. (February 29). Revised December 23, 1997Google Scholar
- . Generalized goal programming: Polynomial methods and applications. Math. Programming (2002) 93:281–303Crossref, Google Scholar
- Normal-boundary intersection: A new method for generating Pareto optimal points in nonlinear multicriteria optimization problems. SIAM J. Optim. (1998) 8(3):631–657Crossref, Google Scholar
- . A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optim. (1997) 14(1):63–69Crossref, Google Scholar
- . Approximation techniques for the set of efficient points. (2001) . Professorial dissertation, Fachbereich Mathematik, Universität Dortmund, Dortmund, Germany. (January 31)Google Scholar
- . Gap-free computation of Pareto-points by quadratic scalarizations. Math. Methods Oper. Res. (2004) 59:69–89Crossref, Google Scholar
- . Constructing approximations to the efficient set of convex quadratic multiobjective problems. (2002) . Ergebnisberichte Angewandte Mathematik 211, Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany. (January). ForthcomingGoogle Scholar
- Proper efficiency and the theory of vector maximization. J. Optim. Theory Appl. (1968) 22:618–630Google Scholar
- . Warm start of the primal-dual method applied in the cutting plane scheme. Math. Programming (1998) 83(1):125–143Crossref, Google Scholar
- . Reoptimization with the primal-dual interior point method. SIAM J. Optim. (2003) 13:561–584Google Scholar
- . Warm start and ϵ-subgradients in a cutting plane scheme for block-angular linear programs. Comput. Optim. Appl. (1999) 14(1):17–36Crossref, Google Scholar
- . Vektoroptimierung—Theorie, Verfahren und Anwendungen. Mathematisch-Naturwissenschaftliche Bibliothek (1990) 74(B. G. Teubner Verlagsgesellschaft, Leipzig, Germany) Google Scholar
- . Sensitivity analyis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors. (2003) . AdvOl-report 2003/6, Advanced Optimization Laboratory, McMaster University, Hamilton, Ontario, Canada. (December)Google Scholar
- Haimes Y. Y., Steuer Ralph E. Research and practice in multiple criteria decision making. Lecture Notes in Economics and Mathematical Systems (2000) 487(Springer Verlag, Berlin, Germany) Google Scholar
- , Branke Jürgen, Deb Kalyanmoy, Miettinen Kaisa, Steuer Ralph E. A new adaptive algorithm for convex quadratic multicriteria optimization. Practical Approaches to Multi-Objective Optimization. Dagstuhl Seminar Proceedings (2004) (Schloß Dagstuhl, Germany)Google Scholar
- . Bestimmung effizienter Portefeuilles durch Warmstart-Innere-Punkt-Methoden. (2000) . Diplomarbeit, Lehrstuhl für Wissenschaftliches Rechnen, Fachbereich Mathematik, Universität Dortmund, Dortmund, GermanyGoogle Scholar
- . Warmstart-Strategien in der parametrisierten Optimierung mit Anwendung in der multikriteriellen Optimierung. (2005) . Ph.D. thesis, Lehrstuhl für Wissenschaftliches Rechnen, Fachbereich Mathematik, Universität Dortmund, Dortmund, GermanyGoogle Scholar
- . Nonlinear multiobjective optimization: A generalized homotopy approach. International Series of Numerical Mathematics (2001) 25(Birkhäuser Verlag, Berlin, Germany) Google Scholar
- Horst R., Pardalos P.Handbook of Global Optimization (1995) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
- Global Optimization: Deterministic Approaches (1993) 2nd ed.(Springer, Berlin, Germany) Crossref, Google Scholar
- . Mathematical Vector Optimization in Partially Ordered Linear Spaces (1986) (Verlag Peter Lang, Frankfurt, Germany) Google Scholar
- . Vector Optimization: Theory, Applications and Methods (2004) (Springer Verlag, Berlin, Germany) Crossref, Google Scholar
- A bicriterial optimization problem of antenna design. Comput. Optim. Appl. (1997) 7:261–276Crossref, Google Scholar
- Köksalan M., Zionts S. Multiple criteria decision making in the new millennium. Proc. 15th Internat. Conf. Multiple Criteria Decision Making (MCDM) (2001) Ankara, Turkey, 2000(Springer Verlag, Berlin, Germany) Crossref, Google Scholar
- Mean-Variance Analysis in Portfolio Choice and Capital Markets (1987) (Basil Blackwell Ltd., Oxford, UK) Google Scholar
- Portfolio Selection, Efficient Diversification of Investments (1991) 2nd ed.(Basil Blackwell Ltd., Oxford, UK) Google Scholar
- Cutting plane methods for conic programs. SIAM Conf. Optim. (2005) . (May)Google Scholar
- . Interior-point polynomial algorithms in convex programming. SIAM Stud. Appl. Math. (1994) 13(Society for Industrial and Applied Mathematics, Philadelphia, PA) Crossref, Google Scholar
- A second-order cone cutting surface method: Complexity and application. (2005) . Available at http://www.optimization-online.org (May 11)Google Scholar
- . Linear Programming, Complexity Theory and Elementary Functional Analysis (1994) . Published as [32], (June)Google Scholar
- . Linear programming, complexity theory and elementary functional analysis. Math. Programming (1995) 70A:279–351Crossref, Google Scholar
- . A mathematical view of interior-point methods for convex optimizations. MPS-SIAM Ser. Optim. (2001) . Philadelphia, PAGoogle Scholar
- . Algorithms for Portfolio Optimization and Portfolio Insurance (1994) (Paul Haupt, Bern, Switzerland) Google Scholar
- . Theory of multiobjective optimization. Mathematics in Science and Engineering (1985) 176(Academic Press, Inc., Orlando, FL) Google Scholar
- Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM Rev. (2001) 43(1):31–85Crossref, Google Scholar
- A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements. Math. Comput. (1999) 68:1347–1378Crossref, Google Scholar
- Sensitivity analysis in linear programming and semidefinite programming using interior-point method. Math. Programming (2001) 90:229–261Crossref, Google Scholar
- Warm-start strategies in interior-point methods for linear programming. SIAM J. Optim. (2002) 12:782–810Crossref, Google Scholar

