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Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column…
The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
This paper introduces a framework for super-resolution of scalable video based on compressive sensing and sparse representation of residual frames in reconnaissance and surveillance applications. We exploit efficient compressive sampling…
This paper concerns two algorithms for solving optimal control problems with hybrid systems. The first algorithm aims at hybrid systems exhibiting sliding modes. The first algorithm has several features which distinguishes it from the other…
The study of online algorithms with machine-learned predictions has gained considerable prominence in recent years. One of the common objectives in the design and analysis of such algorithms is to attain (Pareto) optimal tradeoffs between…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Top-k queries have been studied intensively in the database community and they are an important means to reduce query cost when only the "best" or "most interesting" results are needed instead of the full output. While some optimality…