Monomial-wise Optimal Separable Underestimators for Mixed-Integer Polynomial Optimization

In this paper we introduce a new method for solving box-constrained mixed-integer polynomial problems to global optimality. The approach, a specialized branch-and-bound algorithm, is based on the computation of lower bounds provided by the minimization of separable underestimators of the polynomial objective function. The underestimators are the novelty of the approach because the standard approaches … Read more

On the Incomplete Oblique Projections Method for Solving Box Constrained Least Squares Problems

The aim of this paper is to extend the applicability of the incomplete oblique projections method (IOP) previously introduced by the authors for solving inconsistent linear systems to the box constrained case. The new algorithm employs incomplete projections onto the set of solutions of the augmented system Ax-r= b, together with the box constraints, based … Read more

A New Framework for Combining Global and Local Methods in Black Box Optimization

We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a … Read more

A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization

We propose a procedure for building symmetric positive definite band preconditioners for large-scale symmetric, possibly indefinite, linear systems, when the coefficient matrix is not explicitly available, but matrix-vector products involving it can be computed. We focus on linear systems arising in Newton-type iterations within matrix-free versions of projected methods for bound-constrained nonlinear optimization. In this … Read more

On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods

When solving the general smooth nonlinear optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy $\epsilon$ can be obtained by a second-order method using cubic regularization in at most $O(\epsilon^{-3/2})$ problem-functions evaluations, the same order bound as in the unconstrained case. This result is obtained by first showing that the … Read more

Subspace accelerated matrix splitting algorithms for bound-constrained quadratic programming and linear complementarity problems

This paper studies the solution of two problems—bound-constrained quadratic programs and linear complementarity problems—by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations … Read more

An algorithm for the choice of the regularization parameter in inverse problems in imaging

In this paper we present an iterative algorithm for the solution of regularization problems arising in inverse image processing. The regularization function to be minimized is constituted by two terms, a data fit function and a regularization function, weighted by a regularization parameter. The proposed algorithm solves the minimization problem and estimates the regularization parameter … Read more

On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds

We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. … Read more

An Iterative algorithm for large size Least-Squares constrained regularization problems.

In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from … Read more

A quasi-Newton projection method for nonnegatively constrained image deblurring

In this paper we present a quasi-Newton projection method for image deblurring. The mathematical problem is a constrained minimization problem, where the objective function is a regularization function and the constraint is the positivity of the solution. The regularization function is a sum of the Kullback-Leibler divergence, used to minimize the error in the presence … Read more