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An improved definition of proper efficiency for vector maximization with respect to cones. (English) Zbl 0418.90081

MSC:
90C31Sensitivity, stability, parametric optimization
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Full Text: DOI
References:
[1] Benson, H. P.: Efficiency and proper efficiency in vector maximization with respect to cones. Research publication GMR-2557 (1977) · Zbl 0357.90059
[2] Benson, H. P.: Existence of efficient solutions for vector maximization problems. J. optimization theory appl. 26, 569-580 (1978) · Zbl 0373.90085
[3] Borwein, J.: Proper efficient points for maximizations with respect to cones. SIAM J. Control optimization 15, 57-63 (1977) · Zbl 0369.90096
[4] Canon, M. D.; Jr., C. D. Cullum; Polak, E.: Theory of optimal control and mathematical programming. (1970) · Zbl 0264.49001
[5] Geoffrion, A. M.: Proper efficiency and the theory of vector maximization. J. math. Anal. appl. 22, 618-630 (1968) · Zbl 0181.22806
[6] Kelley, J. L.: Linear topological spaces. (1963) · Zbl 0115.09902
[7] Varaiya, P. P.: Nonlinear programming in Banach space. SIAM J. Appl. math. 15, 284-293 (1967) · Zbl 0171.18004
[8] Wendell, R. E.; Lee, D. N.: Efficiency in multiple objective optimization problems. Math. programming 12, 406-414 (1977) · Zbl 0362.90092
[9] Wijsman, R. A.: Convergence of sequences of convex sets, cones and functions. Bull. amer. Math. soc. 70, 186-188 (1964) · Zbl 0121.39001
[10] Wijsman, R. A.: Convergence of sequences of convex sets, cones and functions, II. Trans. amer. Math. soc. 123, 32-45 (1966) · Zbl 0146.18204
[11] Yu, P. L.: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. J. optimization theory appl. 14, 319-377 (1974) · Zbl 0268.90057