Related papers: Computing Experiment-Constrained D-Optimal Designs
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. Let…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with…