Related papers: A Semismooth Newton Method for Tensor Eigenvalue C…

In this paper, a new definition of tensor p-shrinkage nuclear norm (p-TNN) is proposed based on tensor singular value decomposition (t-SVD). In particular, it can be proved that p-TNN is a better approximation of the tensor average rank…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a…

In this paper, we develop a new framework for constructing infeasible-start primal-dual methods for Conic Optimization. Our approach can be seen as a straightforward consequence of Gordan Theorem of Alternative. Given by the target upper…

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…

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 develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and…

In this paper, we introduce set-valued tensor complementarity problem where the elements of the involved tensors are defined based on a set-valued mapping. We study several properties of the solution set under the framework of set-valued…

The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved…

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

In this paper, we propose a novel tensor-based Dinkelbach--Type method for computing extremal tensor generalized eigenvalues. We show that the extremal tensor generalized eigenvalue can be reformulated as a critical subproblem of the…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…

We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…

This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…

In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

We study properties of the central path underlying a nonlinear semidefinite optimization problem, called NSDP for short. The latest radical work on this topic was contributed by Yamashita and Yabe (2012): they proved that the Jacobian of a…

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…