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Found 13 papers, 1 papers with code
Higher-Order Newton Methods with Polynomial Work per Iteration
At each step, our $d^{\text{th}}$-order method uses semidefinite programming to construct and minimize a sum of squares-convex approximation to the $d^{\text{th}}$-order Taylor expansion of the function we wish to minimize.
Safely Learning Dynamical Systems
For $T=2$, we give a semidefinite representation of the set of safe initial conditions and show that $\lceil n/2 \rceil$ trajectories generically suffice for safe learning.
Sums of Separable and Quadratic Polynomials
We establish that the answer to question (i) is positive for univariate plus quadratic polynomials and for convex SPQ polynomials, but negative already for bivariate quartic SPQ polynomials.
Safely Learning Dynamical Systems from Short Trajectories
For our first two results, we consider the setting of safely learning linear dynamics.
Learning Dynamical Systems with Side Information
We then demonstrate the added value of side information for learning the dynamics of basic models in physics and cell biology, as well as for learning and controlling the dynamics of a model in epidemiology.
Complexity aspects of local minima and related notions
We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials.
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 that finds a point within Euclidean distance $c^n$ (for any constant $c \ge 0$) of a local minimizer of an $n$-variate quadratic function over a polytope.
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 application of semidefinite programming in fields such as machine learning, control, and robotics.
On the Complexity of Detecting Convexity over a Box
As a byproduct, our proof shows that the problem of testing whether all matrices in an interval family are positive semidefinite is strongly NP-hard.
Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies"
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 extended abstract [4] and slides in [3].
DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied.
Geometry of 3D Environments and Sum of Squares Polynomials
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials.
DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials.
