Optimization and Variational Analysis

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Description

Optimization or, more generally, modern variational analysis, can be viewed as emerging from the calculus of variations and mathematical programming. One of the most characteristic features of this discipline is the intrinsic presence of nonsmoothnees, that is, the necessity to deal with nondifferentiable functions, sets with nonsmooth boundaries, and set-valued mappings. In fact, even the simplest problems in optimal control are intrinsically nonsmooth, in contrast to the classical calculus of variations. This is mainly due to pointwise constraints on control functions that often take only discrete values as in typical problems of automatic control.

 

Variational analysis and optimization cover many techniques coming from different mathematical fields such as: topology, convex analysis, integral and differential calculus, linear algebra, among others.

  

Publications

  • Briceño, L., Hoang, N. D. & Peypouquet, J. (2016). "Existence, stability and optimality for optimal control problems governed by maximal monotone operators". Journal of Differential Equations, 260(1), 733-757. [More] 
  • Lopez, J. & Maldonado, S. (2016). "Multi-class second-order cone programming support vector machines". Information Sciences, 330, 328-341. [More] 
  • L., B. (2015). “Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions”. Optimization, 64, 1239-1261. [More] 
  • Henríquez, A., Osses, A., Gallardo, L. & Díaz Resquín, M. (2015). "Analysis and optimal design of air quality monitoring networks using a variational approach". Tellus B, Chemical and Physical Meteorology, 67. [More] 
  • Piazza, A. & Roy, S. (2015). "Deforestation and optimal management". JOURNAL OF ECONOMIC DYNAMICS & CONTROL, 53, 15-27. [More]