Browsing by Author "Parrilo, Pablo A."
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The 2013 Newton Institute Programme on polynomial optimization
Letchford, Adam N; Lasserre, Jean B; Steurer, David; Letchford, Adam N.; Lasserre, Jean B.; e.a. (Springer Berlin Heidelberg, 201503)The rapidly growing field of polynomial optimisation (PO) is concerned with optimisation problems in which the objective and constraint functions are all polynomials. There are applications of PO in a surprisingly wide ... 
Analysis of the Joint Spectral Radius Via Lyapunov Functions on PathComplete Graphs
Ahmadi, Amir Ali; Jungers, Raphael M.; Parrilo, Pablo A.; Roozbehani, Mardavij (Association for Computing Machinery (ACM), 201104)We study the problem of approximating the joint spectral radius (JSR) of a finite set of matrices. Our approach is based on the analysis of the underlying switched linear system via inequalities imposed between multiple ... 
Approximate cone factorizations and lifts of polytopes
Gouveia, Joao; Parrilo, Pablo A.; Thomas, Rekha R. (SpringerVerlag, 201412)In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis ... 
Bandgap Optimization of TwoDimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods
Men, Han; Nguyen, Ngoc Cuong; Freund, Robert Michael; Parrilo, Pablo A.; Peraire, Jaime (Elsevier, 201001)In this paper, we consider the optimal design of photonic crystal structures for twodimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinitedimensional Hermitian ... 
Basis selection for SOS programs via facial reduction and polyhedral approximations
Permenter, Frank Noble; Parrilo, Pablo A. (Institute of Electrical and Electronics Engineers (IEEE), 201502)We develop a monomial basis selection procedure for sumofsquares (SOS) programs based on facial reduction. Using linear programming and polyhedral approximations, the proposed technique finds a face of the SOS cone ... 
Certifying Unstability of Switched Systems Using Sum of Squares Programming
Legat, Benoît; Parrilo, Pablo A.; Jungers, Raphaël (Society for Industrial & Applied Mathematics (SIAM), 2020)© 2020 Society for Industrial and Applied Mathematics The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears ... 
A Characterization of Lyapunov Inequalities for Stability of Switched Systems
Jungers, Raphael M.b.; Ahmadi, Amir A; Parrilo, Pablo A.; Roozbehani, Mardavij (Institute of Electrical and Electronics Engineers (IEEE), 201705)We study stability criteria for discretetime switched systems and provide a metatheorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs ... 
Chordal Networks of Polynomial Ideals
Cifuentes, Diego Fernando; Parrilo, Pablo A. (Society for Industrial & Applied Mathematics (SIAM), 201701)We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among ... 
Competitive scheduling in wireless collision channels with correlated channel state
Parrilo, Pablo A.; Candogan, Utku Ozan; Menache, Ishai; Ozdaglar, Asuman E. (Institute of Electrical and Electronics Engineers, 200906)We consider a wireless collision channel, shared by a finite number of mobile users who transmit to a common base station. Each user wishes to optimize its individual network utility that incorporates a natural tradeoff ... 
A Complete Characterization of the Gap between Convexity and SOSConvexity
Ahmadi, Amir Ali; Parrilo, Pablo A. (Society for Industrial and Applied Mathematics, 201305)Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity, its first order characterization, and its ... 
Constrained Consensus and Optimization in MultiAgent Networks
Nedic, Angelia; Ozdaglar, Asuman E.; Parrilo, Pablo A. (Institute of Electrical and Electronics Engineers, 201004)We present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with timevarying connectivity. Our framework is general in that this value can represent ... 
Converse results on existence of sum of squares Lyapunov functions
Ahmadi, Amir Ali; Parrilo, Pablo A. (Institute of Electrical and Electronics Engineers (IEEE), 201203)Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of dynamical systems, the converse question of whether sos Lyapunov functions exist whenever polynomial Lyapunov functions exist has remained ... 
The convex algebraic geometry of linear inverse problems
Chandrasekaran, Venkat; Recht, Benjamin; Parrilo, Pablo A.; Willsky, Alan S. (Institute of Electrical and Electronics Engineers (IEEE), 201009)We study a class of illposed linear inverse problems in which the underlying model of interest has simple algebraic structure. We consider the setting in which we have access to a limited number of linear measurements of ... 
Convex Graph Invariants
Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. (Society for Industrial and Applied Mathematics, 201208)The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are ... 
Design of photonic crystals with multiple and combined band gaps
Men, Han; Nguyen, Ngoc Cuong; Freund, Robert Michael; Lim, K. M.; Parrilo, Pablo A.; e.a. (American Physical Society, 201104)We present and use an algorithm based on convex conic optimization to design twodimensional photonic crystals with large absolute band gaps. Among several illustrations we show that it is possible to design photonic ... 
Diagonal and lowrank decompositions and fitting ellipsoids to random points
Saunderson, James F.; Parrilo, Pablo A.; Willsky, Alan S. (Institute of Electrical and Electronics Engineers (IEEE), 201312)Identifying a subspace containing signals of interest in additive noise is a basic system identification problem. Under natural assumptions, this problem is known as the Frisch scheme and can be cast as decomposing an n × ... 
Diagonal and LowRank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
Saunderson, James F.; Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S. (Society for Industrial and Applied Mathematics, 201212)In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and ... 
Dimension reduction for semidefinite programs via Jordan algebras
Permenter, Frank Noble; Parrilo, Pablo A. (Springer Berlin Heidelberg, 201903)We propose a new method for simplifying semidefinite programs (SDP) inspired by symmetry reduction. Specifically, we show if an orthogonal projection map satisfies certain invariance conditions, restricting to its range ... 
Dynamics in nearpotential games
Candogan, Utku Ozan; Koksal, Asuman E.; Parrilo, Pablo A (Elsevier, 201307)We consider discretetime learning dynamics in finite strategic form games, and show that games that are close to a potential game inherit many of the dynamical properties of potential games. We first study the evolution ... 
Efficient classification of complete parameter regions based on semidefinite programming
Kuepfer, Lars; Sauer, Uwe; Parrilo, Pablo A. (BioMed Central Ltd, 200701)Background: Current approaches to parameter estimation are often inappropriate or inconvenient for the modelling of complex biological systems. For systems described by nonlinear equations, the conventional approach is to ...