Related papers: Recovering the Optimal Solution by Dual Random Pro…
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…
Super-resolution is a fundamental problem in computer vision which aims to overcome the spatial limitation of camera sensors. While significant progress has been made in single image super-resolution, most algorithms only perform well on…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into…
This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{find} \; x\in L\cap\mathbb{R}^n_{+} \;\;\;\; \text{ and } \;…
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…
The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of…
We consider the problem of computationally-efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…
In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment…