A nonmonotone trust-region method for the solution of nonlinear systems of equations with box constraints is considered. The method differs from existing trust-region methods both in using a new nonmonotonicity strategy in order to accept the current step and by using a new updating technique for the trust-region-radius. The overall method is shown to be globally convergent. Moreover, when comb...

The main purpose of this study is to propose, then analyze, and later test a spectral gradient algorithm for solving a convex minimization problem. The considered problem covers the matrix ℓ2,1-norm regularized least squares which is widely used in multi-task learning for capturing the joint feature among each task. To solve the problem, we firstly minimize a quadratic approximated model of the...

We present deterministic nonmonotone learning strategies for multilayer perceptrons (MLPs), i.e., deterministic training algorithms in which error function values are allowed to increase at some epochs. To this end, we argue that the current error function value must satisfy a nonmonotone criterion with respect to the maximum error function value of the M previous epochs, and we propose a subpr...

A new method is introduced for large scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented usi...

We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are “derivativefree” both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals...

Most existing submodular maximization algorithms provide theoretical guarantees with approximation bounds. However, in many cases, users may be interested in an anytime algorithm that can offer a flexible tradeoff between computation time and optimality guarantees. In this paper, we propose a filtered search (FS) framework that allows the user to set an arbitrary approximation bound guarantee w...

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

Nonmonotone missing data arise routinely in empirical studies of social and health sciences, and when ignored, can induce selection bias and loss of efficiency. In practice, it is common to account for nonresponse under a missing-at-random assumption which although convenient, is rarely appropriate when nonresponse is nonmonotone. Likelihood and Bayesian missing data methodologies often require...