A Semismooth Conjugate Gradients Method — Theoretical Analysis

In large scale applications, deterministic and stochastic variants of Cauchy’s steepest descent method are widely used for the minimization of objectives that are only piecewise smooth. In this paper we analyse a  deterministic descent method based on the generalization of rescaled conjugate gradients proposed by Philip Wolfe in 1975 for objectives that are convex. Without … Read more

Optimality conditions for the nonlinear programming problems on Riemannian manifolds

In recent years, many traditional optimization methods have been successfully generalized to minimize objective functions on manifolds. In this paper, we first extend the general traditional constrained optimization problem to a nonlinear programming problem built upon a general Riemannian manifold $\mathcal{M}$, and discuss the first-order and the second-order optimality conditions. By exploiting the differential geometry … Read more