Emre Alper YILDIRIM

Lecturer in Operational Research

School of Mathematics

The University of Edinburgh

Research Overview

My research interests encompass several facets of convex and nonconvex optimization, including theory, algorithms, and applications. I am particularly interested in developing optimization models with desirable structural properties for various real-life applications, exploiting problem-specific properties to develop effective solution methods, understanding the worst-case behaviour of such algorithms, and implementation of algorithms. On the theoretical side, my recent research interests focus on exact and approximate representations of discrete and nonconvex optimization problems via convex conic optimization. My work on applications includes problems arising from electricity markets, wireless networks, logistics, graph theory, and machine learning.

Journal Publications (in Reverse Chronological Order)

  1. E. Alper Yildirim. An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs. Journal of Global Optimization, 2021. DOI: 10.1007/s10898-021-01066-3 (Open Access)
  2. Jacek Gondzio and E. Alper Yildirim. Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations. Journal of Global Optimization, 2021. DOI: 10.1007/s10898-021-01017-y (Open Access)
  3. Y. Gorkem Gokmen and E. Alper Yildirim. On standard quadratic programs with exact and inexact doubly nonnegative relaxations. Mathematical Programming, 2021. DOI: 10.1007/s10107-020-01611-0 (Open Access)
  4. Gunes Erdogan and E. Alper Yildirim. Exact and heuristic algorithms for the carrier-vehicle traveling salesman problem. Transportation Science, 55 (1), pp. 101-121, 2021. DOI: 10.1287/trsc.2020.0999
  5. Ali Yesilcimen and E. Alper Yildirim. An alternative polynomial-sized formulation and an optimization based heuristic for the reviewer assignment problem. European Journal of Operational Research, 276 (2), pp. 436-450, 2019. DOI: 10.1016/j.ejor.2019.01.035
  6. E. Alper Yildirim. Inner approximations of completely positive reformulations of mixed binary quadratic programs: A unified analysis. Optimization Methods and Software, 32 (6), pp. 1163-1186, 2017. DOI: 10.1080/10556788.2016.1245732
  7. Refail Kasimbeyli and E. Alper Yildirim. Optimality conditions in nonconvex and nonsmooth optimization revisited. Pure and Applied Functional Analysis, 2 (1), pp. 99-109, 2017. Paper
  8. Kagan Gokbayrak and E. Alper Yildirim. Exact and heuristic approaches based on noninterfering transmissions for joint gateway selection, time slot allocation, routing and power control for wireless mesh networks. Computers & Operations Research, 81, pp. 102-118, 2017. DOI: 10.1016/j.cor.2016.09.021
  9. Gizem Sagol and E. Alper Yildirim. Analysis of copositive optimization based linear programming bounds on standard quadratic optimization. Journal of Global Optimization, 63 (1), pp. 37-59, 2015. DOI: 10.1007/s10898-015-0269-4
  10. Emre Mengi, E. Alper Yildirim, and Mustafa Kilic. Numerical optimization of eigenvalues of Hermitian matrix functions. SIAM Journal on Matrix Analysis and Applications, 35 (2), pp. 699-724, 2014. DOI: 10.1137/130933472
  11. Immanuel M. Bomze, Stefan Gollowitzer, and E. Alper Yildirim. Rounding on the standard simplex: Regular grids for global optimization. Journal of Global Optimization, 59 (2-3), pp. 243-258, 2014. DOI: 10.1007/s10898-013-0126-2 (Winner of the Journal of Global Optimization Best Paper Award for a paper published in 2014)
  12. Kagan Gokbayrak and E. Alper Yildirim. Joint gateway selection, transmission slot assignment, routing and power control for wireless mesh networks. Computers & Operations Research, 40 (7), pp. 1671-1679, 2013. DOI: 10.1016/j.cor.2012.12.018
  13. Esra Koca and E. Alper Yildirim. A hierarchical solution approach for a multicommodity distribution problem under a special cost structure, Computers & Operations Research, 39 (11), pp. 2612-2624, 2012. DOI: 10.1016/j.cor.2012.01.007
  14. E. Alper Yildirim. On the accuracy of uniform polyhedral approximations of the copositive cone. Optimization Methods and Software, 27 (1), pp. 155-173, 2012. DOI: 10.1080/10556788.2010.540014
  15. Piyush Kumar and E. Alper Yildirim. A linearly convergent linear-time first-order algorithm for support vector classification with a core set result. INFORMS Journal on Computing, 23 (3), pp. 377-391, 2011. DOI: 10.1287/ijoc.1100.0412
  16. E. Alper Yildirim. A simpler characterization of a spectral lower bound on the clique number. Mathematical Methods of Operations Research, 71 (2), pp. 267-281, 2010. DOI: 10.1007/s00186-009-0295-4
  17. Piyush Kumar and E. Alper Yildirim. An algorithm and a core set result for the weighted Euclidean one-center problem. INFORMS Journal on Computing, 21 (4), pp. 614-629, 2009. DOI: 10.1287/ijoc.1080.0315
  18. Piyush Kumar and E. Alper Yildirim. Computing minimum volume enclosing axis-aligned ellipsoids. Journal of Optimization Theory and Applications, 136 (2), pp. 211-228, 2008. DOI: 10.1007/s10957-007-9295-9
  19. S. Damla Ahipasaoglu and E. Alper Yildirim. Identification and elimination of interior points for the minimum enclosing ball problem. SIAM Journal on Optimization, 19 (3), pp. 1392-1396, 2008. DOI: 10.1137/080727208
  20. Elizabeth John and E. Alper Yildirim. Implementation of warm-start strategies in interior-point methods for linear programming in fixed dimension. Computational Optimization and Applications, 41 (2), pp. 151 - 183, 2008. DOI: 10.1007/s10589-007-9096-y
  21. E. Alper Yildirim. Two algorithms for the minimum enclosing ball problem. SIAM Journal on Optimization, 19 (3), pp. 1368-1391, 2008. DOI: 10.1137/070690419
  22. Michael J. Todd and E. Alper Yildirim. On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids. Discrete and Applied Mathematics, 155 (13), pp. 1731-1744, 2007. DOI: 10.1016/j.dam.2007.02.013
  23. E. Alper Yildirim and Xiaofei Fan-Orzechowski. On extracting maximum stable sets in perfect graphs using Lovasz's theta function. Computational Optimization and Applications, 33 (2-3), pp. 229-247, 2006. DOI: 10.1007/s10589-005-3060-5
  24. E. Alper Yildirim. On the minimum volume covering ellipsoid of ellipsoids. SIAM Journal on Optimization, 17 (3) pp. 621-641, 2006. DOI: 10.1137/050622560 (Winner of the 2006 INFORMS Optimization Society Young Researcher Prize)
  25. Piyush Kumar and E. Alper Yildirim. Minimum volume enclosing ellipsoids and core sets. Journal of Optimization Theory and Applications, 126 (1), pp. 1-21, 2005. DOI: 10.1007/s10957-005-2653-6
  26. E. Alper Yildirim. Unifying optimal partition approach to sensitivity analysis in conic optimization. Journal of Optimization Theory and Applications, 122 (2), pp. 405-423, 2004. DOI: 10.1023/B:JOTA.0000042528.76868.22
  27. Piyush Kumar, Joseph S. B. Mitchell, and E. Alper Yildirim. Approximate minimum enclosing balls in high dimensions using core-sets. Journal of Experimental Algorithmics, Vol. 8, Article 1, 2003. DOI: 10.1145/996546.996548 (Special issue devoted to selected papers from the Fifth Workshop on Algorithm Engineering and Experiments (ALENEX03))
  28. E. Alper Yildirim. An interior-point perspective on sensitivity analysis in semidefinite programming. Mathematics of Operations Research, 28 (4), pp. 649-676, 2003. DOI: 10.1287/moor.28.4.649.20511
  29. E. Alper Yildirim and Stephen J. Wright. Warm-start strategies in interior-point methods for linear programming. SIAM Journal on Optimization, 12 (3), pp. 782-810, 2002. DOI: 10.1137/S1052623400369235
  30. E. Alper Yildirim and Michael J. Todd. An interior-point approach to sensitivity analysis in degenerate linear programs. SIAM Journal on Optimization, 12 (3), pp. 692-714, 2002. DOI: 10.1137/S1052623400382455
  31. E. Alper Yildirim and Michael J. Todd. Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Mathematical Programming, 90 (2), pp. 229-261, 2001. DOI: 10.1007/PL00011423

Refereed Conference Proceedings

  1. Piyush Kumar, Joseph S. B. Mitchell, and E. Alper Yildirim. Computing core-sets and approximate smallest enclosing hyperspheres in high dimensions. Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments (ALENEX03), pp. 45 - 55, 2003. Paper