A novel adaptive stepsize for proximal gradient method solving mixed variational inequality problems and applications

In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm use a novel adaptive stepsize which is proved to be increasing to a positive limitation. The weak convergence and strong convergence with R-linear rate of our new algorithm … Read more

A mixed-integer exponential cone programming formulation for feature subset selection in logistic regression

Logistic regression is one of the widely-used classification tools to construct prediction models. For datasets with a large number of features, feature subset selection methods are considered to obtain accurate and interpretable prediction models, in which irrelevant and redundant features are removed. In this paper, we address the problem of feature subset selection in logistic … Read more

A Unifying Framework for Sparsity Constrained Optimization

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … Read more

Sparse Recovery via Partial Regularization: Models, Theory and Algorithms

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear system. We … Read more

Sparse Approximation via Penalty Decomposition Methods

In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-“norm” of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of … Read more

Penalty Decomposition Methods for hBcNorm Minimization

In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent rank minimization problem and then apply the penalty decomposition (PD) method proposed in [33] to solve the latter problem. By utilizing … Read more