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We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\le d$ orthogonal directions, where d is the dimension of the ambient space. These ...${}^{}$$\mathrm{}\mathrm{}$

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank–Wolfe algorithm and its variants already avoid projections, ...$$$\mathcal{}{}^{\mathrm{}}$

In this paper, we seek a new modification way to ensure the positiveness of the conjugate parameter and, based on the Dai-Yuan (DY) method in the vector setting, propose an associated family of conjugate gradient (CG) methods with guaranteed ...

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic ...$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$$\sqrt{}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$

In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function f and a convex (possibly non-smooth ...$$$\mathrm{}$