Abstract
This paper is a contribution to the unified approach of Halkin, Neustadt, Gamkrelidze and others to the theory of necessary conditions for general optimization problems.
The basic problem is formulated in terms of real linear topological spaces, mappings between them and a partial ordering determined by a proper convex cone. It includes, therefore, problems with both scalar- and vector-valued optimality criteria.
Optimality conditions are developed in terms of Gâteaux and Fréchet differentials of given mappings and linear continuous functionals on the spaces concerned, making use of the Dubovitskiy and Milyutin's formalism.
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References
Dubovitskiy A.Ya., and Milyutin A.A., Extremum Problems in the Presence of Restrictions, (USSR) Journal of Computational Mathematics and Mathematical Physics, Vol. 5, No. 1, 1965.
Halkin H., A Satisfactory Treatment of Equality and Operator Constraints in the Dubovitskii-Milyutin Optimizational Formalism, Journal of Optimization Theory and Applications, Vol. 6, No. 2, 1970.
Neustadt L.W., A General Theory of Extremals, Journal of Computer and System Sciences, Vol. 3, No. 1, 1969.
Vlach M., On Necessary Conditions of Optimality in Linear Spaces, Comment. Math. Univ. Carolinae, Vol. 11, No. 3, 1970.
Nonlinear Functional Analysis, Proceedings of an Advanced Seminar, Ed. L.B. Rall, Academic Press, 1971.
Neustadt L.W., An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems, I General Theory, SIAM Journal on Control, Vol. 4, No. 3, 1966.
Neustadt L.W., An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems, II Applications, SIAM Journal on Control, Vol. 5, No. 1, 1967.
Bazaraa M.S. and Goode J.J., Necessary Optimality Criteria in Mathematical Programming in Normed Linear Spaces, Journal of Optimization Theory and Applications, Vol. 11, No. 3, 1973.
Craven B.D., Nonlinear Programming in Locally Convex Spaces, Journal of Optimization Theory and Applications, Vol. 10, No. 4, 1972.
Virsan C., Necessary Conditions for Optimization Problems with Operational Constraints, SIAM Journal on Control, Vol. 8, No. 4, 1970.
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© 1976 Springer-Verlag Berlin Heidelberg
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Rigby, L. (1976). Contribution to Dubovitskiy and Milyutin's optimization formalism. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 2. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07623-9_303
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DOI: https://doi.org/10.1007/3-540-07623-9_303
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