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Normed convex processes. (English) Zbl 0264.47018


MSC:

47A50 Equations and inequalities involving linear operators, with vector unknowns
15A39 Linear inequalities of matrices
54C60 Set-valued maps in general topology
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
65K05 Numerical mathematical programming methods
52Bxx Polytopes and polyhedra
90C99 Mathematical programming
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References:

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[3] David Gale, The theory of linear economic models, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960.
[4] Alan J. Hoffman, On approximate solutions of systems of linear inequalities, J. Research Nat. Bur. Standards 49 (1952), 263 – 265.
[5] Функционал\(^{\приме}\)ный анализ в нормированных пространствах, Государств. Издат. Фис.-Мат. Лит., Мосцощ, 1959 (Руссиан). · Zbl 0127.06102
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[7] Stephen M. Robinson, Bounds for error in the solution set of a perturbed linear program, Linear Algebra and Appl. 6 (1973), 69 – 81. · Zbl 0283.90028
[8] Stephen M. Robinson, Extension of Newton’s method to nonlinear functions with values in a cone, Numer. Math. 19 (1972), 341 – 347. · Zbl 0227.65040 · doi:10.1007/BF01404880
[9] R. Tyrrell Rockafellar, Monotone processes of convex and concave type, Memoirs of the American Mathematical Society, No. 77, American Mathematical Society, Providence, R.I., 1967. · Zbl 0189.19602
[10] -, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1970.
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