Abstract
We are concerned with methods for solving the problem
where the (possibly nonsmooth) functions f and F are realvalued and convex on RN, hi are affine and |I| < ∞. We assume that the feasible set S=Sh ∩ SF is nonempty, where Sh = {x: hi(x) ≤ 0 , i ∈ I} and SF={x: F(x)≤ 0}, and that F( \(\tilde x\)) < 0 for some \(\tilde x\) in Sh(the Slater condition). We suppose that for each x ∈ Sh one can compute f(x), F(x) and two arbitrary subgradients gf(x) ∈ ∂f(x) and gF(x) ∈ ∂f(x); these evaluations are not required for x ∉ Sh.
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Kiwiel, K.C. (1985). Descent Methods for Nonsmooth Convex Constrained Minimization. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_19
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DOI: https://doi.org/10.1007/978-3-662-12603-5_19
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