Related papers: Global Optimality Characterizations and Algorithms…
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, we develop a new concept of Global Curvature Bound for an arbitrary nonlinear operator between abstract metric spaces. We use this notion to characterize the global complexity of high-order algorithms solving composite…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
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}…
We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster…
This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…