Related papers: Optimal matroid bases with intersection constraint…
While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of $2$ for the \emph{unweighted} matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted…
Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
Binary polynomial optimization is equivalent to the problem of minimizing a linear function over the intersection of the multilinear set with a polyhedron. Many families of valid inequalities for the multilinear set are available in the…
Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
We consider a stochastic inventory control problem under censored demands, lost sales, and positive lead times. This is a fundamental problem in inventory management, with significant literature establishing near-optimality of a simple…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
We study the Minimum Submodular-Cost Allocation problem (MSCA). In this problem we are given a finite ground set $V$ and $k$ non-negative submodular set functions $f_1 ,..., f_k$ on $V$. The objective is to partition $V$ into $k$ (possibly…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We consider the problem of covering multiple submodular constraints. Given a finite ground set $N$, a cost function $c: N \rightarrow \mathbb{R}_+$, $r$ monotone submodular functions $f_1,f_2,\ldots,f_r$ over $N$ and requirements…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 = (V,…
A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…