Search

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 satisfies 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. [ABSTRACT FROM AUTHOR]

In this study we derive the order of convergence of some line search techniques based on fitting polynomials, using function values only. It is shown that the order of convergence increases with the degree of the polynomial. If viewed as a sequence, the orders approach the Golden Section Ratio when the degree of the polynomial tends to infinity. [ABSTRACT FROM AUTHOR]