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Zbl 0846.90085
Kiwiel, Krzysztof C.
The efficiency of subgradient projection methods for convex optimization. II: Implementations and extensions. (English)
[J] SIAM J. Control Optimization 34, No.2, 677-697 (1996). ISSN 0363-0129; ISSN 1095-7138/e

Summary: In the first part of this paper [see the preceding review] we studied subgradient methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates of the optimal value. We presented several variants and showed that they enjoy almost optimal efficiency estimates. In this part of the paper, we discuss possible implementations of such methods. In particular, their projection subproblems may be solved inexactly via relaxation methods, thus opening the way for parallel implementations. We discuss accelerations of relaxation methods based on simultaneous projections, surrogate constraints, and conjugate and projected (conditional) subgradient techniques.

MSC 2000:: *90C25 Convex programming
65Y05 Parallel computation (numerical methods)
65K05 Mathematical programming (numerical methods)

Keywords: nondifferentiable optimization; successive projections; linear inequalities; efficiency estimates; relaxation methods; parallel implementations; surrogate constraints; subgradient techniques

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