Journal of Global Optimization Best Paper Award for 2015
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly...
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| Veröffentlicht in: | Journal of global optimization 2016-12, Vol.66 (4), p.595-596 |
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| container_title | Journal of global optimization |
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| creator | Butenko, Sergiy |
| description | In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly constrained nonconvex problems. For optimization problems of the above structure, we propose random coordinate descent algorithms and analyze their convergence properties. For the general case, when the objective function is nonconvex and composite we prove asymptotic convergence for the sequences generated by our algorithms to stationary points and sublinear rate of convergence in expectation for some optimality measure. Additionally, if the objective function satises an error bound condition we derive a local linear rate of convergence for the expected values of the objective function. We also present extensive numerical experiments for evaluating the performance of our algorithms in comparison with state-of-the-art methods. |
| doi_str_mv | 10.1007/s10898-016-0479-4 |
| format | Article |
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| issn | 0925-5001 1573-2916 |
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| subjects | Algorithms Awards & honors Committees Computer Science Convex analysis Editorial Editorials Mathematics Mathematics and Statistics Nominations Operations Research/Decision Theory Optimization Optimization algorithms Real Functions |
| title | Journal of Global Optimization Best Paper Award for 2015 |
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