Abstract
In this contribution we are going to discuss the extension of the method of feasible directions[1],[2],[3] to programming problems involving an infinite number of constraints. Problems of this type arise frequently in applications. We shall be working with arbitrary convex approximations instead of with linearizations, simply to emphasize the fact that the feasible direction method belongs to that class of methods where not differentiability but rather convex-likeness of the functions involved is the essential property.
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References
M. Frank, P. Wolfe: An algorithm for quadratic programming. Naval Res. Logistics Quart.3 (1956), 95–110.
G. Zoutendijk: Methods of Feasible Directions. Elsevier, Amsterdam, 1960.
H. P. Kiinzi, W. Oettli: Nichtlineare Optimierung (Lecture Notes in Operations Research and Mathematical Systems, 16), pp. 65–70. Springer, Berlin, 1969.
O. Pironneau, E. Polak: On the rate of convergence of certain methods of centers. Math. Programming 2 (1972), 230–257;
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© 1975 Springer-Verlag Berlin Heidelberg
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Blum, E., Oettli, W. (1975). An Extension of the Method of Feasible Directions. In: Marchuk, G.I. (eds) Optimization Techniques IFIP Technical Conference. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-38527-2_38
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DOI: https://doi.org/10.1007/978-3-662-38527-2_38
Publisher Name: Springer, Berlin, Heidelberg
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