## Existence theorems for Pareto optimization; multivalued and Banach space valued functionals.(English)Zbl 0393.49004

### MSC:

 49J27 Existence theories for problems in abstract spaces 49J35 Existence of solutions for minimax problems 49J45 Methods involving semicontinuity and convergence; relaxation
Full Text:

### References:

 [1] Leonard D. Berkovitz, Lower closure and existence theorems in optimal control, International Conference on Differential Equations (Proc., Univ. Southern California, Los Angeles, Calif., 1974) Academic Press, New York, 1975, pp. 26 – 39. · Zbl 0243.93012 [2] A. Blaquière (Editor), Topics in differential games, North-Holland, Amsterdam, 1973. · Zbl 0265.00029 [3] N. Bourbaki, Espaces vectoriels topologiques, Chapters I, II, Hermann, Paris, 1955. MR 14, 880. · Zbl 0066.35301 [4] Lamberto Cesari, Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints. I, Trans. Amer. Math. Soc. 124 (1966), 369 – 412. · Zbl 0145.12501 [5] L. Cesari, Geometric and analytic views in existence theorems for optimal control in Banach spaces. I. Distributed parameters, J. Optimization Theory Appl. 14 (1974), 505 – 520. Collection of articles dedicated to Magnus R. Hestenes. · Zbl 0272.49002 [6] Lamberto Cesari, Lower semicontinuity and lower closure theorems without seminormality conditions, Ann. Mat. Pura Appl. (4) 98 (1974), 381 – 397. · Zbl 0281.49006 [7] Lamberto Cesari, Closure theorems for orientor fields and weak convergence, Arch. Rational Mech. Anal. 55 (1974), 332 – 356. · Zbl 0296.49029 [8] Lamberto Cesari, Sobolev spaces and multidimensional Lagrange problems of optimization., Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 193 – 227. · Zbl 0186.48901 [9] Lamberto Cesari, Existence theorems for optimal controls of the Mayer type, SIAM J. Control 6 (1968), 517 – 552. · Zbl 0174.14301 [10] Lamberto Cesari and David E. Cowles, Existence theorems in multidimensional problems of optimization with distributed and boundary controls, Arch. Rational Mech. Anal. 46 (1972), 321 – 355. · Zbl 0246.49005 [11] L. Cesari and M. B. Suryanarayana, Closure theorems without seminormality conditions, J. Optimization Theory Appl. 15 (1975), 441 – 465. Existence theory in the calculus of variations and optimal control. · Zbl 0279.49010 [12] L. Cesari and M. B. Suryanarayana, Nemitsky’s operators and lower closure theorems, J. Optimization Theory Appl. 19 (1976), no. 1, 165 – 183. Existence theorem issue. · Zbl 0305.49016 [13] -, Existence theorems for Pareto problems of optimization, Conf. Calculus of Variations, and Control Theory, Math. Research Center, Madison, Wis., 1975. [14] M. Connors and D. Teichrow, Optimal control of dynamic operations research models, Internat. Textbook, Scranton, Pa., 1967. · Zbl 0159.48801 [15] N. O. Da Cunha and E. Polak, Constrained minimization under vector-valued criteria in linear topological spaces, Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) Academic Press, New York, 1967, pp. 96 – 108. · Zbl 0223.49012 [16] Mahlon M. Day, Normed linear spaces, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg;, 1962. · Zbl 0100.10802 [17] Graham Jameson, Ordered linear spaces, Lecture Notes in Mathematics, Vol. 141, Springer-Verlag, Berlin-New York, 1970. · Zbl 0196.13401 [18] P. J. Kaiser, Existence theorems in the calculus of variations, Ph.D. thesis, Univ. of Michigan, 1973. [19] P. J. Kaiser and M. B. Suryanarayana, Orientor field equations in Banach spaces, J. Optimization Theory Appl. 19 (1976), no. 1, 141 – 183. Existence theorem issue. · Zbl 0305.49018 [20] V. L. Klee Jr., Convex sets in linear spaces. II, Duke Math. J. 18 (1951), 875 – 883. · Zbl 0044.11201 [21] Интеграл$$^{\приме}$$ные операторы в пространствах суммируемых функций, Издат. ”Наука”, Мосцощ, 1966 (Руссиан). · Zbl 0145.39703 [22] E. J. McShane and R. B. Warfield Jr., On Filippov’s implicit functions lemma, Proc. Amer. Math. Soc. 18 (1967), 41 – 47. · Zbl 0145.34403 [23] J. J. Moreau, Convexity and duality, Functional Analysis and Optimization, Academic Press, New York, 1966, pp. 145 – 169. [24] Czesław Olech, Lexicographical order, range of integrals and ”bang-bang” principle, Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) Academic Press, New York, 1967, pp. 35 – 45. · Zbl 0225.49038 [25] C. Olech, Weak lower semicontinuity of integral functionals, J. Optimization Theory Appl. 19 (1976), no. 1, 3 – 16. Existence theorem issue. · Zbl 0305.49019 [26] V. Pareto, Course d’economie politique, Lausanne, Rouge, 1896. [27] Steve Smale, Global analysis and economics. I. Pareto optimum and a generalization of Morse theory, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 531 – 544. [28] M. B. Suryanarayana, Remarks on lower semicontinuity and lower closure, J. Optimization Theory Appl. 19 (1976), no. 1, 125 – 140. Existence theorem issue. · Zbl 0305.49017 [29] H. F. Weinberger, Conditions for local Pareto optima (to appear). [30] P. L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optimization Theory Appl. 14 (1974), 319 – 377. · Zbl 0268.90057 [31] P. L. Yu and G. Leitmann, Nondominated decisions and cone convexity in dynamic multicriteria decision problems, J. Optimization Theory Appl. 14 (1974), 573 – 584. Collection of articles dedicated to Magnus R. Hestenes. · Zbl 0273.90003 [32] L. A. Zadeh, Optimality and nonscalar valued performance criteria, IEEE Trans. Automatic Control AC-8 (1963), 59-60. [33] Jean-Pierre Aubin, A Pareto minimum principle, Differential Games and Related Topics (Proc. Internat. Summer School, Varenna, 1970) North-Holland, Amsterdam, 1971, pp. 147 – 175. [34] L. Cesari and M. B. Suryanarayana, An existence theorem for Pareto problems, Nonlinear Anal. 2 (1978), no. 2, 225 – 233. · Zbl 0383.49003 [35] M. B. Suryanarayana, Remarks on existence theorems for Pareto optimality, Dynamical systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976) Academic Press, New York, 1977, pp. 335 – 347. [36] W. Stadler, A survey of multicriteria optimization, 1977 (preprint). · Zbl 0388.90001 [37] Czesław Olech, Existence theorems for optimal problems with vector-valued cost function, Trans. Amer. Math. Soc. 136 (1969), 159 – 180. · Zbl 0179.14002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.