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05/20/2023
Safely Learning Dynamical Systems
A fundamental challenge in learning an unknown dynamical system is to re...
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05/11/2021
Sums of Separable and Quadratic Polynomials
We study separable plus quadratic (SPQ) polynomials, i.e., polynomials t...
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11/24/2020
Safely Learning Dynamical Systems from Short Trajectories
A fundamental challenge in learning to control an unknown dynamical syst...
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08/23/2020
Learning Dynamical Systems with Side Information
We present a mathematical and computational framework for the problem of...
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08/14/2020
Complexity aspects of local minima and related notions
We consider the notions of (i) critical points, (ii) second-order points...
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08/12/2020
On the complexity of finding a local minimizer of a quadratic function over a polytope
We show that unless P=NP, there cannot be a polynomial-time algorithm th...
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08/14/2019
A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics
Historically, scalability has been a major challenge to the successful a...
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08/12/2018
Time-Varying Semidefinite Programs
We study time-varying semidefinite programs (TV-SDPs), which are semidef...
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06/16/2018
On the Complexity of Detecting Convexity over a Box
It has recently been shown that the problem of testing global convexity ...
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05/09/2018
Robust-to-Dynamics Optimization
A robust-to-dynamics optimization (RDO) problem is an optimization probl...
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03/20/2018
On the Complexity of Testing Attainment of the Optimal Value in Nonlinear Optimization
We prove that unless P=NP, there exists no polynomial time (or even pseu...
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10/09/2017
Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies"
In a recent note [8], the author provides a counterexample to the global...
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09/27/2017
On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity
In recent years, techniques based on convex optimization and real algebr...
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06/08/2017
DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
In recent years, optimization theory has been greatly impacted by the ad...
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11/22/2016
Geometry of 3D Environments and Sum of Squares Polynomials
Motivated by applications in robotics and computer vision, we study prob...
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10/06/2015