Presentation of Research Lab :   Analysis, Optimization, Control

version française

Members :  5 full professors, 12 assistant professors + 1 "PRAG", 3 post doc, 3 Ph.D. students

Variational analysis

• Members
  M. Lassonde (resp.), M. Geoffroy, F. Jules

  Themes

  • Sub-differential calculus
  • variational analysis in metric spaces
  • optimal control of differential inclusions

  Expected short-term results

  • Stability of minima and sub-differentials
    (4 papers in progress)
  • sub-differential calculus
    (4 papers in progress, 1 of which accepted)
  • Techniques for variational analysis
    (1 book in progress)

  research perspectives

  • sub-C¹ functions and sub-monotone operators
  • optimal control of obstacle type VI
  • sensibility in optimal control of PDE

Non linear algebraic analysis

• Members
  J.-A. Marti (resp.), S. Bernard, A. Delcroix, M. Hasler, V. Valmorin; E. Allaud (post-doc), V. Dévoué (Ph.D. student)

  Themes

  • Structure of algebras of G.F.
  • Generalized hyperfunctions on the torus
  • GF via periodic situations
  • Applications to non-linear differential problems
  • Prediction of hurricane tracks

  Expected short-term results:

  • caracteristic Cauchy problems
    (1 paper published, 1 paper under way)
  • generalized funciton algebras via sequence spaces
    (2 papers published/in press, 1 paper submitted (with S. Pilipovic))

  Research perspectives

  • Theory of generalized hyperfunctions
  • multiparameter algebras and singular problems
  • Controlability of non linear problems with singular data

Optimization

• Members
  R. Janin (resp.), J.-P. Cherdieu, J.-C. Mado, D.-J. Mercier, J. Narayaninsamy, M. Ranguin; A. Edouard (PRAG); R. Blache (post-doc)

  Themes

  • critical direction in optimal control
  • optimality conditions of order greater than 2
  • quadratic-quadratic programs

  Expected short-term results

  • optimality conditions of ordre 3 and 4 in Rⁿ
    (paper under way with Dedieu)
  • Lax method and Borsuk's theorem
    (paper in progress)

  Research perspectives

  • sub-C¹ functions and sub-monotone operators
  • sensibility in optimal control of PDE

Numerical optimization

• Members
  A. Pietrus (resp.), M. Geoffroy, J.-C. Mado

  Themes

  • multi-valued equations
  • hyperbolic polynomials and applications
  • numerical analysis of PDE

  Expected short-term results

  • Instability of surfaces of constraint materials
    (publication with V. Lods and JM Rakotoson)
  • Polynomial mathematical rogrammation
    (paper in progress)
  • multi valued equations
    (paper in progress)

  research perspectives

  • interior point methods
  • numerical analysis of control problems

Optimal control

• Membres
  O. Nakoulima (resp.), G. Mophou, A. Omrane, J. Velin; G. Malespine (doctorant), R. Dorville (doctorant)

  Themes

  • Control of singular distributed systems
  • Problems of population dynamics

  Expected short-term results

  • Systems with missing data
    (1 accepted, 1 submitted)
  • Multi state systems and ill-posed systems
    (2 submitted, 2 in progress)

  Research perspectives

  • Characterization of singular optimality system
  • Numerical analysis of control problems
  • Modelling of population dynamics

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