Related papers: QUADRO: A supervised dimension reduction method vi…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
The recent availability of quantum annealers as cloud-based services has enabled new ways to handle machine learning problems, and several relevant algorithms have been adapted to run on these devices. In a recent work, linear regression…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and…
Quantum computing holds transformative potential for optimizing large-scale drone fleet operations, yet its near-term limitations necessitate hybrid approaches blending classical and quantum techniques. This work introduces Quantum Unmanned…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
We introduce a new Projected Rayleigh Quotient Iteration aimed at improving the convergence behaviour of classic Rayleigh Quotient iteration (RQI) by incorporating approximate information about the target eigenvector at each step. While…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Model-based derivative-free optimization (DFO) methods are an important class of DFO methods that are known to struggle with solving high-dimensional optimization problems. Recent research has shown that incorporating random subspaces into…
We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct…
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
The univariate dimension reduction (UDR) method stands as a way to estimate the statistical moments of the output that is effective in a large class of uncertainty quantification (UQ) problems. UDR's fundamental strategy is to approximate…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…