Ivanenko, Yevhen

Physical bounds in electromagnetic field theory have been of interest for more than a decade. Considering electromagnetic structures from the system theory perspective, as systems satisfying linearity, time-invariance, causality and passivity, it is possible to characterize their transfer functions via Herglotz functions. Herglotz functions are use...

Weiss, Pierre Escande, Paul Bathie, Gabriel Dong, Yiqiu

We design an image quality measure independent of local contrast changes, which constitute simple models of illumination changes. Given two images, the algorithm provides the image closest to the first one with the component tree of the second. This problem can be cast as a specific convex program called isotonic regression. We provide a few analyt...

Aslan, Y. (author) Puskely, J. (author) Roederer, A.G. (author) Yarovoy, Alexander (author)

Minimization of the maximum sidelobe level for a given array geometry, amplitude distribution and nulling sectors by phase-only adjustment of the element coefficients is studied. Nonlinear optimization problem for phase distribution is solved using a novel iterative convex optimization algorithm which includes mutual coupling effects and exploits s...

Weiss, Pierre Escande, Paul Bathie, Gabriel Dong, Yiqiu

We design an image quality measure independent of contrast changes, which are defined as a set of transformations preserving an order between the level lines of an image. This problem can be expressed as an isotonic regression problem. Depending on the definition of a level line, the partial order between adjacent regions can be defined through cha...

Faybusovich, Leonid Zhou, Cunlu
Published in
Computational Optimization and Applications

We developed a long-step path-following algorithm for a class of symmetric programming problems with nonlinear convex objective functions. The theoretical framework is developed for functions compatible in the sense of Nesterov and Nemirovski with -lndet\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \u...

Lavenant, Hugo Claici, Sebastian Chien, Edward Solomon, Justin

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation of quadratic optimal transport proposed for flat domains by Benamou and Brenier [2000], adapted to discrete su...

Chizat, Lenaic Bach, Francis

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study a simple minimization method: the unknown measure is discretized into a mixture of particles and a continuous...

Fu, Anqi Ungun, Barıṣ Xing, Lei Boyd, Stephen
Published in
Optimization and Engineering

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex re...

Davy, Guillaume Féron, Eric Garoche, Pierre-Loïc Henrion, Didier

Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing fuel-efficient controls. Another approach called optimal control is capable of computing such difficult traject...

Apidopoulos, Vassilis Aujol, Jean-François Dossal, Charles

In this paper we study the convergence of an Inertial Forward-Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that for a sequence of overrrelaxation parameters, that do not satisfy Nesterov’s rule one can still expect some relatively fast convergence properties for the objective function. In addition w...