Related papers: Solving Convex Quadratic Optimization with Indicat…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
We consider mixed-integer quadratic optimization problems with banded matrices and indicator variables. These problems arise pervasively in statistical inference problems with time-series data, where the banded matrix captures the temporal…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
We consider quadratic optimization in variables $(x,y)$ where $0\le x\le y$, and $y\in\{0,1\}^n$. Such binary $y$ are commonly refered to as "indicator" or "switching" variables and occur commonly in applications. One approach to such…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…