This paper deals with an algorithm incorporating the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. The algorithm decomposes a linear program into a main problem and a subprob-lem. The subproblem is solved approximately. Hence, inexact Newton directions are used in solving the main problem. We show that the algorithm is ...

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse representation in a chosen dictionary in time domain. This leads to a large scale convex optimization problem, which involves combined l1-l2 norm minimization. The optimization is carried by the truncated Newton method, using preconditioned conjug...

In this paper, we propose a trust region filter method for minimax problems. Based on the filter technique, the minimax problem is transformed to a constrained optimization problem and solved by the traditional filter idea. In the presented algorithm, the acceptable criterion of the trial points is relaxed, so compared to the existed SQP and Newton-type methods for minimax method, this method i...

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse representation in a chosen dictionary in time domain. This leads to a large scale convex optimization problem, which involves combined l1-l2 norm minimization. The optimization is carried by the truncated Newton method, using preconditioned conjug...

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number of special cases. One proof technique uses recent work of M. Baker on linear systems on graphs, by means of which we reduce our conjecture to a purely combin...

In this paper we use the combination of the global interval Newton method and the method of close returns for detection and proving the existence of periodic orbits in a continuous–time chaotic dynamical system. We consider a simple third order electronic circuit for which we prove the existence of several unstable periodic orbits. We also find out which of these periodic orbits are symmetric a...

The global exponential stability is investigated for neural networks with interval time-varying delays. Based on the Leibniz-Newton formula and linear matrix inequality technique, delay-dependent stability criteria are proposed to guarantee the exponential stability of neural networks with interval time-varying delays. Some numerical examples and comparisons are provided to show that the propos...

We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We de...

In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local convergence results. However, the main contribution of the paper is related to global worst-case complexity bounds for different problem classes including some nonconvex cases. It is shown that the search direction c...

We propose a technique of multisensor signal reconstruction based on the assumption, that source signals are spatially sparse, as well as have sparse [wavelet-type] representation in time domain. This leads to a large scale convex optimization problem, which involves l1 norm minimization. The optimization is carried by the Truncated Newton method, using preconditioned Conjugate Gradients in inn...