Gradient projection and conditional gradient methods for constrained nonconvex minimization
Abstract
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for its solution and to obtain results that guarantee convergence of the algorithm under some minimal natural assumptions. We use the Lezanski-Polyak-Lojasiewicz condition on a manifold to prove the global linear convergence of the algorithm. Another method well fitted for the problem is the conditional gradient (Frank-Wolfe) algorithm. We examine some conditions which guarantee global convergence of full-step version of the method with linear rate.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.11580
- arXiv:
- arXiv:1906.11580
- Bibcode:
- 2019arXiv190611580B
- Keywords:
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- Mathematics - Optimization and Control;
- 49J53;
- 90C26;
- 90C52