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Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
We consider a regularization problem whose objective function consists of a convex fidelity term and a regularization term determined by the $\ell_1$ norm composed with a linear transform. Empirical results show that the regularization with…
Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the…
As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to the regularized optimization, aiming at minimizing the $\ell_0$ norm or its continuous surrogates that characterize the sparsity. From…
Convex regularizers are often used for sparse learning. They are easy to optimize, but can lead to inferior prediction performance. The difference of $\ell_1$ and $\ell_2$ ($\ell_{1-2}$) regularizer has been recently proposed as a nonconvex…
We present a new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer. The main features of the new method include: $(i)$ an evolving set of indices corresponding to variables that are predicted…
This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…
In this paper, we propose $\ell_p$-norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the…
In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…
We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our…
This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines $\ell_0$- and $\ell_1$-regularization. We compute its solution by adapting a recent…
Machine learning algorithms typically require abundant data under a stationary environment. However, environments are nonstationary in many real-world applications. Critical issues lie in how to effectively adapt models under an…
We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…