We consider an iterative computation of negative curvature directions, in largescale unconstrained optimization frameworks, needed for ensuring the convergence toward stationary pointswhich satisfy secondorder necessary optimality conditions. We show that to the latter purpose, we can fruitfully...
Nonlinear Optimization


The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the nonzero components (or the ℓnorm) of the solution. We propose to deal with the ℓnorm by means...


We introduce a class of positive definite preconditioners for the solution of large symmetric indefinite linear systems or sequences of such systems, in optimization frameworks. The preconditioners are iteratively constructed by collecting information on a reduced eigenspace of the indefinite...

In this paper we propose convex and LP bounds for standard quadratic programming (StQP) problems and employ them within a branchandbound approach. We first compare different bounding strategies for StQPs in terms both of the quality of the bound and of the computation times. It turns out that the...


In this work, we deal with Truncated Newton methods for solving large scale (possibly nonconvex) unconstrained optimization problems. In particular,we consider the use of amodified Bunch and Kaufman factorization for solving the Newton equation, at each (outer) iteration of the method. The Bunch...

An implicit filtering algorithm for derivativefree multiobjective optimization with box constraintsThis paper is concerned with the definition of new derivativefree methods for box constrained multiobjective optimization. The method that we propose is a nontrivial extension of the wellknown implicit filtering algorithm to the multiobjective case. Global convergence results are stated under...


Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN), which are semidefinite programs where the elements of the...