Abstract. We analyze an abridged version of the active-set algorithm FPC AS proposed in [20] for solving the l1-regularized problem, i.e., a weighted sum of the l1-norm ‖x‖1 and a smooth function f(x). The active set algorithm alternatively iterates between two stages. In the first “nonmonotone line search (NMLS)” stage, an iterative first-order method based on “shrinkage” is used to estimate t...

We present a novel definition of the reinforcement learning state, actions and reward function that allows a deep Q-network (DQN) to learn to control an optimization hyperparameter. Using Q-learning with experience replay, we train two DQNs to accept a state representation of an objective function as input and output the expected discounted return of rewards, or q-values, connected to the actio...

When solving ill-conditioned nonlinear programs by descent algorithms, the descent requirement may induce the step lengths to become very small, thus resulting in very poor performances. Recently, suggestions have been made to circumvent this problem, among which is a class of approaches in which the objective value may be allowed to increase temporarily. Grippo et al. [GLL91] introduce nonmono...

In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer's approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method. Our approach uses a path search idea to control the descent. After elaborating the single steps, we analyze and p...

Obtaining high-quality machine translations is still a long way off. A postediting phase is required to improve the output of a machine translation system. An alternative is the so called computerassisted translation. In this framework, a human translator interacts with the system in order to obtain high-quality translations. A statistical phrase-based approach to computer-assisted translation ...

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They generally coupled with a nonmonotone linesearch strategy compare well Newton-based large sequences systems. The vector is used as the search direction choosing steplength has crucial impact on performance. In this work we address both theoretically experimentally ...

The conjugate gradient (CG) method is one of the most popular methods for solving smooth unconstrained optimization problems due to its simplicity and low memory requirement. However, the usage of CG methods are mainly restricted in solving smooth optimization problems so far. The purpose of this paper is to present efficient conjugate gradient-type methods to solve nonsmooth optimization probl...

In the era of huge datasets, the top-k search becomes an effective way to decrease the search time of top-k objects. The original top-k search requires a monotone combination function and lists of objects ordered by attribute values. Our approach of the top-k search is motivated by complex user preferences over product catalogues. Such user preferences are composed of the local user preferences...