Javier Peña

Research interests

• Computation of equilibria in large sequential games
• Financial optimization
• Algorithms for convex optimization
• Condition numbers for optimization
• Applications of conic programming

Teaching

• Optimization Methods in Finance (mini-4, 2008)
• Advanced Linear Programming (mini-4, 2008)
• Dynamic Programming (mini-2, 2007)
• Optimization (mini-1, 2007)
• Data Mining (mini-5, 2007)
• Probability (mini-3, 2007)

Working Papers

• S. Hoda, A. Gilpin, and J. Peña " Smoothing techniques for computing Nash equilibria of sequential games''
• A. Gilpin, J. Peña, and T. Sandholm " First-order algorithm with O(ln(1/\epsilon)) convergence for \epsilon-equilibrium in two-person zero-sum games''
• J. Peña, J. Vera, and L. Zuluaga "Static-arbitrage bounds on the prices of basket options via linear programming.''

Published Papers

• D. Cheung, F. Cucker, and J. Peña, "A condition numbers for multifold conic systems,'' 
  SIAM Journal on Optimization 19 (2008) pp. 261--270.
• J. Peña, J. Vera, and L. Zuluaga, "Exploiting equalities in polynomial programming,'' 
  Operations Research Letters 36 (2008) pp. 223--228.
• J. Vera, J. Rivera, J. Peña, Y. Hui, " A primal-dual symmetric relaxation for homogeneous conic systems, "
  Journal of Complexity 23 (2007) pp. 245--261.
• J. Peña, J. Vera, and L. Zuluaga, " Computing the stability number of a graph via linear and semidefinite programming, "
  SIAM Journal on Optimization 18 (2007) pp. 87--105.
  Matlab code for the semidefinite programming approximations to the stability number.
• L. Zuluaga, J. Vera, and J. Peña, " LMI approximations for cones of positive semidefinite forms, "
  SIAM Journal on Optimization 16 (2006) pp. 796--817.
• J. Peña, "On the block-structured distance to non-surjectivity of sublinear mappings,"
  Mathematical Programming 103 (2005) pp. 561--573.
• L. Zuluaga and J. Peña, "A conic programming approach to generalized Tchebycheff inequalities,'' 
  Mathematics of Operations Research 30 (2005) pp. 369--388.
• J. Peña, "Conic systems and sublinear mappings: equivalent approaches,'' 
  Operations Research Letters 32 (2004) pp. 463--467.
• D. Cheung, F. Cucker, and J. Peña, "Unifying condition numbers for linear programming,'' 
  Mathematics of Operations Research 28 (2003) pp. 609--624.
• J. Peña, "A characterization of the distance to infeasibility under structured perturbations," 
  Linear Algebra and its Applications 370 (2003) pp. 193--216.
• J. Peña, "Two properties of condition numbers for convex programs via implicitly defined barrier functions," 
  Mathematical Programming 93 (2002) pp. 55--75.
• F. Cucker and J. Peña. "A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine," 
  SIAM Journal on Optimization 12 (2002) pp. 522--554.
• J. Peña, "Conditioning of convex programs from a primal-dual perspective," 
  Mathematics of Operations Research 26 (2001) pp. 206--220.
• J. Peña, "Understanding the geometry of infeasible perturbations of a conic linear system," 
  SIAM Journal on Optimization 10 (2000) pp. 534--550.
• J. Peña and J. Renegar, "Computing approximate solutions for convex conic systems of constraints," 
  Mathematical Programming 87 (2000) pp. 351--383.

If you would like a copy of any of these papers, please send me email: j f p at andrew dot c m u dot e d u

Recent Presentations

• "Computing the stability number of a graph via linear and semidefinite programming," CIRM, Luminy, Oxford, March 2005.
• "Conditioning in optimization and variational analysis," Oxford University, Oxford, November 2003.
• "On the block-structured distance to ill-posedness," ISMP 2003, Conpenhagen, August 2003.