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We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. First proposed for linear regression in the 1970s, this approach has recently…

Constrained combinatorial optimization problems are frequently reformulated as quadratic unconstrained binary optimization (QUBO) models in order to leverage emerging quantum optimization algorithms such as the Variational Quantum…

Accurate prediction of mRNA secondary structure is critical for understanding gene expression, translation efficiency, and advancing mRNA-based therapeutics. However, the combinatorial complexity of possible foldings, especially in long…

The spatial Sigma-Delta ($\Sigma\Delta$) architecture can be leveraged to reduce the quantization noise and enhance the effective resolution of few-bit analog-to-digital converters (ADCs) at certain spatial frequencies of interest.…

The generalization error bound of support vector machine (SVM) depends on the ratio of radius and margin, while standard SVM only considers the maximization of the margin but ignores the minimization of the radius. Several approaches have…

This paper considers convex quadratic programs associated with the training of support vector machines (SVM). Exploiting the special structure of the SVM problem a new type of active set method with long cycles and stable rank-one-updates…

In this work, we consider strongly convex strongly concave (SCSC) saddle point (SP) problems $\min_{x\in\mathbb{R}^{d_x}}\max_{y\in\mathbb{R}^{d_y}}f(x,y)$ where $f$ is $L$-smooth, $f(.,y)$ is $\mu$-strongly convex for every $y$, and…

We study two important SVM variants: hard-margin SVM (for linearly separable cases) and $\nu$-SVM (for linearly non-separable cases). We propose new algorithms from the perspective of saddle point optimization. Our algorithms achieve…

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…

Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed…

In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply…

We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X =…

We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish computable formulas for these backward errors using a class of minimization problems…

For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a…

In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, facing a challenge of fundamental importance in many topic areas of quantum computing. The algorithm uses a variational quantum circuit…

Spatial covariance matrix (SCM) is essential in many applications of multi-antenna systems such as massive multiple-input multiple-output (MIMO). For massive MIMO operating at millimeter-wave bands, hybrid analog-digital structure has been…

We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…

We introduce two new no-regret algorithms for the stochastic shortest path (SSP) problem with a linear MDP that significantly improve over the only existing results of (Vial et al., 2021). Our first algorithm is computationally efficient…