Related papers: A Scalable Algorithm For Sparse Portfolio Selectio…

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…

We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking…

In the portfolio multiobjective optimization framework, we propose to compare and choose, among all feasible asset portfolios of a given market, the one that maximizes the product of the distances between its values of risk and gain and…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…

We propose a variable smoothing algorithm for solving nonconvexly constrained nonsmooth optimization problems. The target problem has two issues that need to be addressed: (i) the nonconvex constraint and (ii) the nonsmooth term. To handle…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that…

In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…

In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…

Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with…

Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of…