This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globaliz...

Reams of different methods have been applied on the inexact graph matching problem in the last decades. In fact, there are two disjoint groups of approaches, exhaustive search and approximate methods. The first ones guarantee that the best solution is always found while the last ones generally have a significantly reduced time complexity at the expense of accepting sub-optimal solutions. This a...

In this paper we discuss inexact Uzawa algorithms and inexact nonlinear Uzawa algorithms to solve discretized variational inequalities of the second kind. We prove convergence results for the algorithms. Numerical examples are included to show the effectiveness of the algorithms.

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that model partial differential equation, parameter is given form generalized polynomial chaos expansion. The leads to solution eigenvalue problem, and wish characterize rightmost eigenvalue. focus, particular, on problems nonsymmetric...

This paper considers the inexact Barzilai-Borwein algorithm applied to saddle point problems. To this aim, we study the convergence properties of the inexact Barzilai-Borwein algorithm for symmetric positive definite linear systems. Suppose that gk and g̃k are the exact residual and its approximation of the linear system at the k-th iteration, respectively. We prove the R-linear convergence of t...

The Commutative Class of search directions for semidefinite programming is first proposed by Monteiro and Zhang [13]. In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Co...

We consider the problem of identifying motifs, recurring or conserved patterns, in the data modeled as strings or sequences. In particular, we present a new deterministic algorithm for finding patterns that are embedded as exact or inexact instances in all or most of the input strings. The proposed algorithm (1) improves search efficiency compared to existing algorithms, and (2) scales well wit...

A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear...

Various search directions used in interior-point-algorithms for the SDP (semidefinite program) and the monotone SDLCP (semide nite linear complementarity problem) are characterized by the intersection of a maximal monotone a ne subspace and a maximal and strictly antitone a ne subspace. This observation provides a uni ed geometric view over the existence of those search directions.

This paper presents a tensor approximation algorithm, based on the Levenberg–Marquardt method for nonlinear least square problem, to decompose large-scale tensors into sum of products vector groups given scale, or obtain low-rank without losing too much accuracy. An Armijo-like rule inexact line search is also introduced this algorithm. The result decomposition adjustable, which implies that ca...