968 research outputs found
The Chebyshev Hyperplane Optimization Problem
We consider the following problem. Given a finite set of pointsyj inR n we want to determine a hyperplane H such that the maximum Euclidean distance betweenH and the pointsyj is minimized. This problem(CHOP) is a non-convex optimization problem with a special structure. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments
Methods for many-objective optimization: an analysis
Decomposition-based methods are often cited as the
solution to problems related with many-objective optimization. Decomposition-based methods employ a scalarizing function to reduce a many-objective problem into a set of single objective problems, which upon solution yields a good approximation of the set of optimal solutions. This set is commonly referred to as
Pareto front. In this work we explore the implications of using decomposition-based methods over Pareto-based methods from a probabilistic point of view. Namely, we investigate whether there is an advantage of using a decomposition-based method, for example using the Chebyshev scalarizing function, over Paretobased methods
From Cutting Planes Algorithms to Compression Schemes and Active Learning
Cutting-plane methods are well-studied localization(and optimization)
algorithms. We show that they provide a natural framework to perform
machinelearning ---and not just to solve optimization problems posed by
machinelearning--- in addition to their intended optimization use. In
particular, theyallow one to learn sparse classifiers and provide good
compression schemes.Moreover, we show that very little effort is required to
turn them intoeffective active learning methods. This last property provides a
generic way todesign a whole family of active learning algorithms from existing
passivemethods. We present numerical simulations testifying of the relevance
ofcutting-plane methods for passive and active learning tasks.Comment: IJCNN 2015, Jul 2015, Killarney, Ireland. 2015,
\<http://www.ijcnn.org/\&g
Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem
We consider a recent coinfection model for Tuberculosis (TB), Human
Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome
(AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663].
We introduce and analyze a multiobjective formulation of an optimal control
problem, where the two conflicting objectives are: minimization of the number
of HIV infected individuals with AIDS clinical symptoms and coinfected with
AIDS and active TB; and costs related to prevention and treatment of HIV and/or
TB measures. The proposed approach eliminates some limitations of previous
works. The results of the numerical study provide comprehensive insights about
the optimal treatment policies and the population dynamics resulting from their
implementation. Some nonintuitive conclusions are drawn. Overall, the
simulation results demonstrate the usefulness and validity of the proposed
approach.Comment: This is a preprint of a paper whose final and definite form is with
'Computational and Applied Mathematics', ISSN 0101-8205 (print), ISSN
1807-0302 (electronic). Submitted 04-Feb-2016; revised 11-June-2016 and
02-Sept-2016; accepted for publication 15-March-201
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