相关论文: On the Semidefinite Representability of Continuous…

We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct…

A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…

We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the 1 -minimization in…

Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…

We show how to bound the accuracy of a family of semi-definite programming relaxations for the problem of polynomial optimization on the hypersphere. Our method is inspired by a set of results from quantum information known as quantum de…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

This paper is concerned with a class of zero-norm regularized piecewise linear-quadratic (PLQ) composite minimization problems, which covers the zero-norm regularized $\ell_1$-loss minimization problem as a special case. For this class of…

We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…

The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…

Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…

We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many…

We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…

We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions…

In many contexts one encounters Hermitian operators $M$ on a Hilbert space whose dimension is so large that it is impossible to write down all matrix entries in an orthonormal basis. How does one determine whether such $M$ is positive…