5 research outputs found

    Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution

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    We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this problem, obtained by randomization. The relaxation gap is proved to converge to zeros as N goes to infinity, independently of the dimension of the aggregate. We propose a stochastic method to construct an approximate minimizer of the original problem, given an approximate solution of the randomized problem. McDiarmid's concentration inequality is used to quantify the probability of success of the method. We consider the Frank-Wolfe (FW) algorithm for the resolution of the randomized problem. Each iteration of the algorithm requires to solve a subproblem which can be decomposed into N independent optimization problems. A sublinear convergence rate is obtained for the FW algorithm. In order to handle the memory overflow problem possibly caused by the FW algorithm, we propose a stochastic Frank-Wolfe (SFW) algorithm, which ensures the convergence in both expectation and probability senses. Numerical experiments on a mixed-integer quadratic program illustrate the efficiency of the method.Comment: 25 pages, 3 figure

    Mean field optimization problems: stability results and Lagrangian discretization

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    We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions \mu with a prescribed marginal mm. The cost function depends on an aggregate term, which is the expectation of \mu with respect to a contribution function. This problem is of particular interest in the context of Lagrangian potential mean field games (MFGs) and their discretization. We provide a first-order optimality condition and prove strong duality. We investigate stability properties of the MFO problem with respect to the prescribed marginal, from both primal and dual perspectives. In our stability analysis, we propose a method for recovering an approximate solution to an MFO problem with the help of an approximate solution to an MFO with a different marginal mm, typically an empirical distribution. We combine this method with the stochastic Frank-Wolfe algorithm of a previous publication of ours to derive a complete resolution method

    La gesti贸n de la descentralizaci贸n y la reforma del transporte Lima - Callao en el a帽o 2020

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    La investigaci贸n titulada la gesti贸n de la descentralizaci贸n y la reforma del transporte Lima - Callao en el a帽o 2020 El presente estudio permiti贸 con贸cer la realidad de la gesti贸n de la descentralizaci贸n y su relaci贸n con la reforma del transporte espec铆ficamente para Lima y Callao esto permiti贸 analizar, el desempe帽o que se ha llevado en gestiones de descentralizaci贸n en materia de transporte, aquello nos permiti贸 abordar el tema con alternativas de soluci贸n, debatiendo sobre lo que se ha actuado de tal manera que se encuentre el equilibrio de conformidad y satisfacci贸n de los usuarios as铆 como de quienes rigen y tiene la facultad de decidir de c贸mo se manejan las pol铆ticas de transporte. Se abordaron en este estudio adem谩s de las formas de administraci贸n, otras disciplinas intervinientes y que no han tenido la relevancia correspondiente que coadyuvaron a la reforma del transporte y contribuyeron a una mejor calidad de prestaci贸n del servicio, siempre en beneficio de la ciudadan铆a, el estudio pudo verificar que el Per煤 no es el 煤nico pa铆s en la regi贸n con reformas del sector transporte impulsado por la descentralizaci贸n, se ha demostrado en la verificaci贸n y recolecci贸n de informaci贸n que estamos en pleno desarrollo de reformas importante

    Industrial Robotics

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    This book covers a wide range of topics relating to advanced industrial robotics, sensors and automation technologies. Although being highly technical and complex in nature, the papers presented in this book represent some of the latest cutting edge technologies and advancements in industrial robotics technology. This book covers topics such as networking, properties of manipulators, forward and inverse robot arm kinematics, motion path-planning, machine vision and many other practical topics too numerous to list here. The authors and editor of this book wish to inspire people, especially young ones, to get involved with robotic and mechatronic engineering technology and to develop new and exciting practical applications, perhaps using the ideas and concepts presented herein
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