TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares

The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions from … Read more

A Derivative-Free Algorithm for the Least-square minimization

Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Under suitable conditions, we establish the global convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm … Read more

A Redistributed Proximal Bundle Method for Nonconvex Optimization

Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , , ,

Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not of the objective function … Read more

Verifiable conditions of $\ell_1hBcrecovery for sparse signals with sign restrictions

Categories Statistics Tags ,

We propose necessary and sufficient conditions for a sensing matrix to be “$s$-semigood” — to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect $\ell_1$-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult … Read more

Optimal Security Response to Attacks on Open Science Grids

Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Control Applications Tags , , , ,

Cybersecurity is a growing concern, especially in open grids, where attack propagation is easy because of prevalent collaborations among thousands of users and hundreds of institutions. The collaboration rules that typically govern large science experiments as well as social networks of scientists span across the institutional security boundaries. A common concern is that the increased … Read more

An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems

Categories Convex Optimization, Data-Mining, Semi-definite Programming Tags , , ,

The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. … Read more

A Bi-directional Resource-bounded Dynamic Programming Approach for the Traveling Salesman Problem with Time Windows

Categories Network Optimization Tags , ,

This paper presents a bi-directional resource-bounded label setting algorithm for the traveling salesman problem with time windows, in which the objective is to minimize travel times. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant … Read more

A Bi-directional Resource-bounded Dynamic Programming Approach for the Traveling Salesman Problem with Time Windows

Categories Network Optimization Tags , ,

This paper presents a bi-directional resource-bounded label setting algorithm for the traveling salesman problem with time windows, in which the objective is to minimize travel times. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant … Read more

Solving the Sensor Network Localization Problem using an Heuristic Multistage Approach

Categories Bound-constrained Optimization, Telecommunications

The Sensor Network Localization Problem (SNLP), arising from many applied fields related with environmental monitoring, has attracted much research during the last years. Solving the SNLP deals with the reconstruction of a geometrical structure from incomplete pairwise distances between sensors. In this paper we present an heuristic multistage approach in which the solving strategy is … Read more

Convergent relaxations of polynomial optimization problems with non-commuting variables

Categories Basic Sciences Applications, Linear, Cone and Semidefinite Programming Tags , , ,

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we introduce a hierarchy … Read more