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Zbl 0846.90084
Kiwiel, Krzysztof C.
The efficiency of subgradient projection methods for convex optimization. I: General level methods. (English)
[J] SIAM J. Control Optimization 34, No.2, 660-676 (1996). ISSN 0363-0129; ISSN 1095-7138/e

Summary: We study subgradient methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates for the optimal value. We present several variants and show that they enjoy almost optimal efficiency estimates. In another 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. They can also exploit 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; parallel computing; subgradient methods; convex optimization; relaxation methods

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