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Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
In this paper, we are interested in the existence of Pareto solutions to vector polynomial optimization problems over a basic closed semi-algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first introduce…
The visible capability is critical in many robot applications, such as inspection and surveillance, etc. Without the assurance of the visibility to targets, some tasks end up not being complete or even failing. In this paper, we propose a…
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…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
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…
Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization…
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning,…
In the recent past, automatic selection or combination of kernels (or features) based on multiple kernel learning (MKL) approaches has been receiving significant attention from various research communities. Though MKL has been extensively…
There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner…
A combinatorial optimization problem (COP) has a finite groundset $E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family $T\in E$ of feasible subsets with objective to find $t\in T$ with maximal weight:…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…