Introducing nonpolyhedral cones to multiobjective programming

Lecture Notes in Economics and Mathematical Systems

Volumn 618, Issue , 2009, Pages 35-45

  Engau, Alexander ^a   Wiecek, Margaret M ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b NONE

Author keywords

Conic scalarization; Domination cones; Multiobjective programming; Positively homogeneous functions

Indexed keywords

EID: 60649111914     PISSN: 00758442     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-85646-7_4     Document Type: Article

References (22)

1. Benson HP (1978) Existence of efficient solutions for vector maximization problems. J Optim Theory Appl 26(4):569-580
2. Cambini A, Luc DT, Martein L (2003) Order-preserving transformations and applications. J Optim Theory Appl 118(2):275-293
3. Ehrgott M (2005) Multicriteria optimization, 2nd edn. Springer, Berlin
4. Ehrgott M, Wiecek MM (2005) Multiobjective programming. In: Figueira J et al (eds) Multiple criteria decision analysis (Int Ser Oper Res Management Sci 78). Springer, New York, pp 667-722
5. Eiehfelder G (2006) Parametergesteuerte Lösung nichtlinearer multikriterieller Optimierungsprobleme. Dissertation, Universität Erlangen-Nürnberg, Germany
6. General Algebraic Modeling System (GAMS) web site: Conic programming in GAMS. Http://www.gams.com/conic/
7. Geoffrion AM (1968) Proper efficiency and the theory of vector maximization. J Math. Anal Appl 22(3):618-630
8. Gerth C, Weidner P (1990) Nonconvex separation theorems and some applications in vector optimization. J Optim Theory Appl 67(2):297-320
9. Guddat J, Guerra Vasquez F, Tammer K, Wendler K (1985) Multiobjective and stochastic optimization based on parametric optimization (Math Res 26). Akademie-Verlag, Berlin
10. Hunt BJ, Wiecek MM (2003) Cones to aid decision making in multicriteria programming. In: Tanino T et al (eds) Multiobjective programming and goal programming (Adv Soft Comput). Springer, Berlin, pp 153-158
11. Isac G, Bahya AO (2002) Full nuclear cones associated to a normal cone. Application to Pareto efficiency. Appl Math Lett 15(5):633-639
12. Jahn J (2004) Vector optimization. Theory, applications, and extensions. Springer, Berlin
13. Lobo MS, Vandenberghe L, Boyd. S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl 284(1-3):193-228
14. Lotov AV, Bushenkov VA, Kamenev GK (2004) Interactive decision maps. Approximation and visualization of Pareto frontier (Appl Optim 89). Kluwer, Boston.
15. Noghin VD (1997) Relative importance of criteria: a quantitative approach. J MultiCrit Dec Anal 6:355-363
16. Pascoletti A, Serafini P (1984) Scalarizing vector optimization problems. J Optim Theory Appl 42(4):499-524
17. Phelps RR (1993) Convex functions, monotone operators and differentiability. Lecture Notes in Math 1364, 2nd edn, Springer, Berlin
18. Rockafellar RT, Wets RJ-B ( 1998) Variational analysis (Grandlehren Math Wiss [Fundamental Principles of Mathematical Sciences], No. 317). Springer, Berlin
19. Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization (Math Sci Eng No. 176). Academic Press, Orlando, FL
20. Weidner P (2003) Tradeoff directions and dominance sets. In: Tanino T et al (eds) Multiobjective programming and goal programming (Adv Soft Comput). Springer, Berlin, pp 275-280
21. Yu P-L (1974) Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. J Optim Theory Appl 14:319-377
22. Yu P-L (1985) Multiple-criteria decision making. Concepts, techniques, and extensions (Math Concepts Methods Sci Eng No. 30). Plenum, New York