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UQ Software
Description:
The goal of my sessions are to help attendees 'hit the ground running' by working through simple case studies with the MIT Uncertainty Quantification (MUQ) library. Those attending these sessions will be given interactive IPython notebooks to allow for hands-on experimentation. We will have one session on forward UQ, focused on Monte Carlo, poly...
Creator:
Parno, Matthew (Massachusetts Institute of Technology)
Created:
2015-06-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
UQ Software
Numerical models for America's Cup yacht design
Description:
In this talk, I will present an overview of the numerical models that have been developed during the last few years for the performance prediction of America's Cup yachts. Different aspects which characterize the behaviour of racing boats will be discussed, such as the role of the yacht appendages, the dynamical response of the yacht in calm and...
Creator:
Parolini, Nicola (Politecnico di Milano)
Created:
2011-03-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Numerical models for America's Cup yacht design
Dynamics in Near-Potential Games
Description:
Potential games are a special class of games that allow for tractable dynamic analysis. Intuitively, games that are 'close' to a potential game should share similar properties. In this talk, we formalize and develop this idea by quantifying how the dynamical features of potential games extend to near-potential games. Towards this goal, we discus...
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2013-10-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Dynamics in Near-Potential Games
Finding Lyapunov functions via convex optimization. Frequency domain descriptions. Kalman-Yakubovich-Popov lemma, Lyapunov proof of gradient methods.
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2014-05-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Finding Lyapunov functions via convex optimization. Frequency domain descriptions. Kalman-Yakubovich-Popov lemma, Lyapunov proof of gradient methods.
From the stable set problem to convex algebraic geometry
Description:
The Lovasz theta body TH(G) is a well-known relaxation of the stable setpolytope STAB(G) that is computable using semidefinite programming. Theseideas can be extended via sum of squares techniques to other combinatorialoptimization problems, providing a natural generalization of the theta bodyfor general polynomial ideals. In this talk we descri...
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2008-11-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
From the stable set problem to convex algebraic geometry
Introduction to dynamical systems. Linear dynamics, stability, Lyapunov functions, eigenvalue conditions.
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2014-05-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Introduction to dynamical systems. Linear dynamics, stability, Lyapunov functions, eigenvalue conditions.
Lyapunov equations and inequalities. Duality in convex optimization and systems theory. Linear matrix inequalities (LMIs). S-Procedure and applications (ellipsoid containment, etc.).
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2014-05-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Lyapunov equations and inequalities. Duality in convex optimization and systems theory. Linear matrix inequalities (LMIs). S-Procedure and applications (ellipsoid containment, etc.).
Sparse Sum-of-squares Certificates on Finite Abelian Groups
Description:
We consider nonnegative functions on abelian groups that are sparse with respect to the Fourier basis. We establish combinatorial conditions on subsets S and T of Fourier basis elements under which nonnegative functions with Fourier support S are sums of squares of functions with Fourier support T. Our combinatorial condition involves constructi...
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2015-05-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Sparse Sum-of-squares Certificates on Finite Abelian Groups
Sums of Squares of Polynomials and SOSTOOLS
Description:
Sum of squares (SOS) programs are a particular class of convex optimizationproblems, that combine in a very appealing way notions from algebraic and numeric computation (in particular, semidefinite programming). They are based on the sum of squares decomposition for multivariate polynomials, and have found many interesting applications, mainly t...
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2006-10-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Sums of Squares of Polynomials and SOSTOOLS
Synthesis: linear quadratic control (LQR), H2 and Hinf optimal control, extensions to nonlinear/decentralized.
Creator:
Parrilo, Pablo A. (Massachusetts Institute of Technology)
Created:
2014-05-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Last Updated:
2018-06-19
Synthesis: linear quadratic control (LQR), H2 and Hinf optimal control, extensions to nonlinear/decentralized.