相关论文: Sum of Squares Basis Pursuit with Linear and Secon…

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…

Chvatal-Gomory (CG) cuts and the Bienstock-Zuckerberg hierarchy capture useful linear programs that the standard bounded degree Lasserre/Sum-of-Squares SOS hierarchy fails to capture. In this paper we present a novel polynomial time SOS…

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P. In a breakthrough paper Fiorini et al. [Proceedings of 44th ACM Symposium on Theory of Computing 2012,…

We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semidefinite programs (SDPs). We exploit a chordal aggregate sparsity pattern…

Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…

The sum-of-squares (SoS) hierarchy is a powerful technique based on semi-definite programming that can be used for both classical and quantum optimization problems. This hierarchy goes under several names; in particular, in quantum…

Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality.…

Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at…

Global optimization has gained attraction over the past decades, thanks to the development of both theoretical foundations and efficient numerical routines. Among recent advances, Kernel Sum of Squares (KernelSOS) provides a powerful…

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…

In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of…

This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…

We introduce a comprehensive framework for analyzing convergence rates for infinite dimensional linear programming problems (LPs) within the context of the moment-sum-of-squares hierarchy. Our primary focus is on extending the existing…

Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in…

In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\ell_\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed…

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…

In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization problems (POPs) and purports that this refutes claims in our…