相关论文: On second-order weak sharp minima of general nonco…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…

This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…

In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…

We consider a class of nonconvex nonsmooth multicomposite optimization problems where the objective function consists of a Tikhonov regularizer and a composition of multiple nonconvex nonsmooth component functions. Such optimization…

We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for…

This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…

Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

In the last two decades, the sequential optimality conditions, which do not require constraint qualifications and allow improvement on the convergence assumptions of algorithms, had been considered in the literature. It includes the work by…