Related papers: Sparse SVM with Hard-Margin Loss: a Newton-Augment…
Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However,…
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…
Support vector machine (SVM) has proved to be a successful approach for machine learning. Two typical SVM models are the L1-loss model for support vector classification (SVC) and $\epsilon$-L1-loss model for support vector regression (SVR).…
The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…
Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regression matrix to effectively capture the intrinsic structure…
Support vector machine is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
We propose a new splitting and successively solving augmented Lagrangian (SSAL) method for solving an optimization problem with both semicontinuous variables and a cardinality constraint. This optimization problem arises in several contexts…
In this paper, we study the embedded feature selection problem in linear Support Vector Machines (SVMs), in which a cardinality constraint is employed, leading to an interpretable classification model. The problem is NP-hard due to the…
Given a dissimilarity matrix, the metric nearness problem is to find the nearest matrix of distances that satisfy the triangle inequalities. This problem has wide applications, such as sensor networks, image processing, and so on. But it is…
Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine…
In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and…
Sparsity-inducing penalties are useful tools to design multiclass support vector machines (SVMs). In this paper, we propose a convex optimization approach for efficiently and exactly solving the multiclass SVM learning problem involving a…
Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on…
We introduce variable projected augmented Lagrangian (VPAL) methods for solving generalized nonlinear Lasso problems with improved speed and accuracy. By eliminating the nonsmooth variable via soft-thresholding, VPAL transforms the problem…
Nonsmooth sparsity constrained optimization encompasses a broad spectrum of applications in machine learning. This problem is generally non-convex and NP-hard. Existing solutions to this problem exhibit several notable limitations,…
Inertial algorithms for minimizing nonsmooth and nonconvex functions as the inertial proximal alternating linearized minimization algorithm (iPALM) have demonstrated their superiority with respect to computation time over their non inertial…
We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely zero-one composite optimization problem (0/1-COP). It is a versatile model including the support…