Publications related to Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Giuseppe Carleo, Julien Sebastian Gacon, Stefan Woerner

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with d parameters, however, is computat ...

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2021

MATHICSE Technical Report: Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

Fabio Nobile, Davide Pradovera

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the param ...

MATHICSE2020

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

Ali H. Sayed, Sulaiman A S A E Alghunaim

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear (exponential) conver ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Florent Gérard Krzakala, Lenka Zdeborová

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Aerodynamic shape optimization via surrogate modelling with convolutional neural networks

Francesco Bardi

Aerodynamic shape optimization has become of primary importance for the aerospace industry over the last years. Most of the method developed so far have been shown to be either computationally very expensive, or to have low dimensional search space. In thi ...

2019

An Optimal Planning Framework to Deploy Self-Reconfigurable Modular Robots

Auke Ijspeert, Mehmet Hasan Mutlu, Simon Lukas Hauser, Hala Khodr, Alexandre Bernardino

Self-reconfiguration is a hard problem due to the high dimensionality of self-reconfigurable modular systems. Searchbased approaches offer complete and optimal solutions. However, naive search algorithms cannot directly solve self-reconfiguration tasks in ...

2019

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

A Novel Iterative Method To Approximate Structured Singular Values

Daniel Kressner

A novel method for approximating structured singular values (also known as values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eigenvalue ...

Siam Publications2017

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Daniel Kressner

A novel method for approximating structured singular values (also known as

\mu

- values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eig ...

MATHICSE2016

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

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Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

MATHICSE Technical Report: Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Aerodynamic shape optimization via surrogate modelling with convolutional neural networks

An Optimal Planning Framework to Deploy Self-Reconfigurable Modular Robots

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

A Novel Iterative Method To Approximate Structured Singular Values

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

MATHICSE Technical Report: Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Aerodynamic shape optimization via surrogate modelling with convolutional neural networks

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

A Novel Iterative Method To Approximate Structured Singular Values

An Optimal Planning Framework to Deploy Self-Reconfigurable Modular Robots