Research

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Interests



Publications

  1. Alvarez, Felipe; Peypouquet, Juan. A unified approach to the asymptotic almost-equivalence of evolution systems without Lipschitz conditions. Nonlinear Analysis: Theory, Methods & Applications 74 (2011), no. 11, 3440-3444. [PDF]  
  2. Alvarez, Felipe; Amaya, Jorge; Griewank, Andreas; Strogies, Nikolai. A continuous framework for open pit mine planning. Mathematical Methods of Operations Research 73 (2011), no. 1, 29-54. [PDF]
  3. Alvarez, Felipe; López, Julio. Convergence to the optimal value for barrier methods combined with Hessian Riemannian gradient flows and generalized proximal algorithms. Journal of Convex Analysis 17 (2010), no. 3&4, 701-720.  [PDF]  
  4. Alvarez, Felipe; Peypouquet, Juan. Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications 73 (2010), no. 9, 3018-3033 [PDF] 
  5. Alvarez, Felipe; López, Julio; Ramírez C., Héctor. Interior proximal algorithm with variable metric for Second-order Cone Programming: Applications to structural optimization and support vector machines. Optimization Methods and Software 25 (2010), no. 6, pages 859-881. [PDF]  
  6. Alvarez, Felipe; Peypouquet, Juan. Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces. Discrete Contin. Dyn. Syst. 25 (2009), no. 4, 1109-1128. [PDF]  
  7. Alvarez, Felipe; Flores, Salvador. Remarks on Lipschitz solutions to measurable differential inclusions and an existence result for some nonconvex variational problems.  J. Convex Anal.  15 (2008), no. 2, 349-363.  [PDF]  
  8. Alvarez, Felipe; Bolte, Jérôme; Munier, Julien. A unifying local convergence result for Newton's method in Riemannian manifolds. Found. Comput. Math. 8 (2008), no. 2, 197--226. [PDF]  
  9. Alvarez, Felipe; Cabot, Alexandre. Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term. Discrete Contin. Dyn. Syst. 15 (2006), no. 3, 921-938. [PDF]  
  10. Alvarez, Felipe; Cabot, Alexandre. On the asymptotic behavior of a system of steepest descent equations coupled by a vanishing mutual repulsion. Recent advances in optimization, 3-17, Lecture Notes in Econom. and Math. Systems, 563, Springer, Berlin, 2006. [PDF]  
  11. Alvarez, Felipe; Carrasco, Miguel; Karine, Pichard. Convergence of a hybrid projection-proximal point algorithm coupled with approximation methods in convex optimization. Math. Oper. Res. 30 (2005), no. 4, 966--984 [PDF]  
  12. Alvarez, Felipe; Carrasco, Miguel. Minimization of the expected compliance as an alternative approach to multiload truss optimization.  Struct. Multidiscip. Optim. 29 (2005), no.6, 470-476 [PDF]  
  13. Alvarez, Felipe; Correa, Rafael; Gajardo, Pedro. Inner estimation of the eigenvalue set and exponential series solutions to differential inclusions.  J. Convex Anal. 12 (2005),  no. 1, 1--11. [PDF]  
  14. Alvarez, Felipe;  Bolte, Jérôme; Brahic, Olivier. Hessian Riemannian gradient flows in convex programming. SIAM J. Control Optim. 43 (2004), no. 2, 477--501. [PDF]  
  15. Alvarez, Felipe; Mandallena, Jean-Philippe. Multiparameter homogenization by localization and blow-up.  Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), no. 5, 801-814. [PDF]  
  16. Alvarez, Felipe; Cabot, Alexandre. Steepest descent with curvature dynamical system.  J. Optim. Theory Appl., 120 (2004), no. 2, 247--273. [PDF]  
  17. Alvarez, Felipe.Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space.  SIAM J. Optim. 14 (2003), no. 3, 773-782. [PDF]  
  18. Alvarez, Felipe;  Attouch, Hédy;  Bolte, Jérôme;  Redont, Patrick. A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics. J. Math. Pures Appl. (9) 81 (2002), no. 8, 747-779. [PDF]  
  19. Alvarez, Felipe; Cominetti, Roberto. Primal and dual convergence of a proximal point exponential penalty method for linear programming. Mathematical Programming. 93 (2002), no. 1, Ser. A, 87-96. [PDF]  
  20. Alvarez, Felipe; Mandallena, Jean-Philippe. Homogenization of multiparameter integrals. Nonlinear Anal. 50 (2002), no. 6, Ser. A: Theory Methods, 839--870.  [PDF]  
  21. Alvarez, Felipe; Attouch, Hédy. Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria. ESAIM Control Optim. Calc. Var. 6 (2001), 539-552. [PS]  
  22. Alvarez, Felipe; Attouch, Hédy. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Wellposedness in optimization and related topics (Gargnano, 1999). Set-Valued Anal. 9 (2001), no. 1-2, 3-11. [PDF]  
  23. Alvarez, Felipe; Attouch, Hédy. The heavy ball with friction dynamical system for convex constrained minimization problems. Optimization (Namur, 1998), 25-35, Lecture Notes in Econom. and Math. Systems, 481, Springer, Berlin, 2000. [PDF]  
  24. Alvarez, Felipe. On the minimizing property of a second order dissipative system in Hilbert spaces. SIAM J. Control Optim. 38 (2000), no. 4, 1102-1119. [PDF]  
  25. Alvarez, Felipe. Absolute minimizer in convex programming by exponential penalty. J. Convex Anal. 7 (2000), no. 1, 197-202. [PDF]  
  26. Alvarez, Felipe; Pérez, José Manuel. A dynamical system associated with Newton's method for parametric approximations of convex minimization problems. Appl. Math. Optim. 38 (1998), no. 2, 193-217. [PDF] 


Projects

  1. Principal Investigator, research grant FONDECYT (CONICYT-Chile) 1050706: “Proximal Iterative Algorithms and Evolution Equations Associated with Penalty Methods in Optimization”, 2005-2009. 
  2. Principal Investigator, research grant FONDECYT (CONICYT-Chile) 1020610: “Discrete and Continuous Approximation of Solutions via Penalty Methods in Constrained Optimization”, 2002-2004. 
  3. Member of the Millennium Science Nucleus “Complex Engineering Systems”, MIDEPLAN-Chile, 2002-2004. 
  4. Principal investigator (Chilean head), project ECOS/CONICYT in Optimization and Equilibrium Problems, Chilean-French Research Cooperation Program,  2000-2002. 
  5. Principal Investigator, research grant FONDECYT (CONICYT-Chile) 1990884: “Dissipative Dynamical Systems and Approximation Methods in Optimization and Variational Problems”, 1999-2001. 
  6. Associate researcher, Centro de Modelamiento Matemático, U. de Chile, project FONDAP in Applied Mathematics (CONICYT-Chile) since March 1999.