Related papers: Efficient Determinant Maximization for All Matroid…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective…
Finding a maximum cardinality common independent set in two matroids (also known as \textsc{Matroid Intersection}) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
Given a matrix $A$ and $k\geq 0$, we study the problem of finding the $k\times k$ submatrix of $A$ with the maximum determinant in absolute value. This problem is motivated by the question of computing the determinant-based lower bound of…
A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing…
Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient…
This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems,…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From…