Publications related to Use of Convex Model Approximations for Real-Time Optimization via Modifier Adaptation

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

Optimization Methods for Control: From Embedded Programmable Hardware to Data-Driven Process Optimization

Harsh Ambarishkumar Shukla

The research community has been making significant progress in hardware implementation, numerical computing and algorithm development for optimization-based control. However, there are two key challenges that still have to be overcome for optimization-base ...

EPFL2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

110th Anniversary: A Feature-Based Analysis of Static Real-Time Optimization Schemes

Dominique Bonvin

This paper addresses the steady-state optimization of continuous processes in the presence of uncertainty in the form of unknown or time-varying model parameters, structural plant-model mismatch, and disturbances. To address these issues, we assume that ce ...

AMER CHEMICAL SOC2019

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...

MATHICSE2018

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

Martand Singhal

Industrial processes are run with the aim of maximizing economic profit while simultaneously meeting process-critical constraints. To this end, model-based optimization can be performed to ensure optimal plant operations. Usually, inevitable model inaccura ...

EPFL2018

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

Volkan Cevher, Anastasios Kyrillidis, Ya-Ping Hsieh, Rabeeh Karimi Mahabadi, Yu-Chun Kao

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of ...

2018

Use of Convex Model Approximations for Real-Time Optimization via Modifier Adaptation

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Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Optimization Methods for Control: From Embedded Programmable Hardware to Data-Driven Process Optimization

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

A first-order primal-dual method with adaptivity to local smoothness

Adaptive Gradient Descent without Descent

110th Anniversary: A Feature-Based Analysis of Static Real-Time Optimization Schemes

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

110th Anniversary: A Feature-Based Analysis of Static Real-Time Optimization Schemes

Adaptive Gradient Descent without Descent

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Optimization Methods for Control: From Embedded Programmable Hardware to Data-Driven Process Optimization

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

A first-order primal-dual method with adaptivity to local smoothness

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization