Abstract
We study the minimization problem f0(x)= min! subject to constraints fi(x)≤ 0,i=1,2,…,k,where each fi=0,1,...,k, is a real convex and subdifferentiable functional on a closed convex set of a reflexive B-space. Supposing that at least one fi,iє{0,1,...,k} is locally uniformly convex,lower bounds for the minimal value of f0 are constructed which do not require the evaluation of the dual functional. It is also shown how in this case an inclusion for the unknown solutions can be obtained.
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Schumacher, K. (1976). Lower Bounds and Inclusion Balls for the Solution of Locally Uniformly Convex Optimization Problems. In: Oettli, W., Ritter, K. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46329-7_24
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DOI: https://doi.org/10.1007/978-3-642-46329-7_24
Publisher Name: Springer, Berlin, Heidelberg
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