Javier Peña

Research interests

• Condition numbers for optimization
• Algorithms for convex optimization
• Equilibria computation
• Financial optimization

Teaching

• Data Mining (MBA)
• Financial Optimization (MSCF)
• Optimization in Finance (MBA)

Published Papers

• I. Briquel, F. Cucker, J. Peña and V. Roshchina, "Fast Computation of Zeros of Polynomial Systems with Bounded Degree under Finite-precision,'' To Appear in Mathematics of Computation.
• J. Peña and V. Roshchina, "A complementarity partition theorem for multifold conic systems,'' To Appear in Mathematical Programming.
• Q. Lin, X. Chen, and J. Peña, "Optimal Regularized Dual Averaging Methods for Stochastic Optimization," Advances in Neural Information Processing Systems (NIPS) (2012).
• N. Soheili and J. Peña, "A smooth perceptron algorithm,'' SIAM Journal on Optimization 22 (2012) pp. 728--737.
• J. Peña, J. Vera, and L. Zuluaga "Computing arbitrage bounds on basket options in the presence of bid-ask spreads,'' European Journal of Operational Research 222 (2012) pp. 369--376.
• 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,'' Mathematical Programming 133 (2012) pp. 279--298.
• J. Peña and H. Sendov, "Spectral self-concordant functions in the space of two by two symmetric matrices," Optimization 60 (2011) pp. 441--449.
• B. Mordukhovich, J. Peña, and V. Roshchina, "Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithms for Matrix Games,'' SIAM Journal on Optimization 20 (2010) pp. 3490--3511.
• J. Peña, X. Saynac, J. Vera, and L. Zuluaga "Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition,'' Algorithmic Operations Research 5 (2010) pp. 65--74.
• J. Peña, J. Vera, and L. Zuluaga, "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance 10 (2010) pp. 819--827.
• J. Peña and H. Sendov, "Separable self-concordant spectral functions and a conjecture of Tunçel," Mathematical Programing 125 (2010) pp. 101--122.
• S. Hoda, A. Gilpin, and J. Peña, and T. Sandholm, "Smoothing techniques for computing Nash equilibria of sequential games,'' Mathematics of Operations Research 35 (2010) pp. 494--512.
• D. Cheung, F. Cucker, and J. Peña, "On strata of degenerate polyhedral cones II: relations between condition measures,'' Journal of Complexity 26 (2010) pp. 209--226.
• L. Zuluaga, J. Peña, and D. Du, "Third-order extensions of Lo's semiparametric bound for European call options," European Journal of Operational Research 198 (2009) pp. 557--570.
• D. Cheung, F. Cucker, and J. Peña, "On strata of degenerate polyhedral cones I: condition and distance to strata,'' European Journal of Operational Research 198 (2009) pp. 23--28.
• J. Peña, "Nash equilibria computation via smoothing techniques," Optima 78 (2008) pp. 12--13.
• C. Jabbour, J. Peña, J. Vera, and L. Zuluaga, "An estimation-free, robust CVaR portfolio allocation model," Journal of Risk 11 (2008) pp. 57--78.
• 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, and 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

• "A modified perceptron algorithm," Fields Institute, Toronto, September 2011.
• "Condition numbers for optimization problems," MOPTA 2011, Lehigh University, August 2011.
• "First-order algorithm with O(ln(1/\epsilon)) convergence for \epsilon-equilibrium in two-person zero-sum games," Institute for Pure and Applied Mathematics, Los Angeles, October 2010.
• "On the distance to ill-posedness," Fields Institute, Toronto, October 2009.
• "Algorithms for computing Nash equilibria of large sequential games," FoCM Conference, Hong Kong, June 2008.

Some Interesting Pointers

• Aimee Kane
• Pittsburgh Jazz Society
• The Cost of Knowledge