E. Alper Yıldırım Home Research Awards and Honours Students and Co-authors Teaching CV

Emre Alper Yıldırım

Reader 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.

Submitted Papers (in Reverse Chronological Order)

  1. Immanuel Bomze, Bo Peng, Yuzhou Qiu, and E Alper Yıldırım. Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization. Submitted, June 2024. arXiv Associated codes: GitHub
  2. Immanuel Bomze, Bo Peng, Yuzhou Qiu, and E Alper Yıldırım. On tractable convex relaxations of standard quadratic optimization problems under sparsity constraints. Submitted, September 2023. arXiv

Journal Publications (in Reverse Chronological Order)

  1. Yuzhou Qiu and E. Alper Yıldırım. On exact and inexact RLT and SDP-RLT relaxations of quadratic programs with box constraints. Journal of Global Optimization, 2024: DOI: 10.1007/s10898-024-01407-y (Open Access) Associated codes: GitHub
  2. Yuzhou Qiu and E. Alper Yıldırım. Polyhedral properties of RLT relaxations of nonconvex quadratic programs and their implications on exact relaxations. Mathematical Programming, 2024. DOI: 10.1007/s10107-024-02070-7 (Open Access)
  3. Fotios Petropoulos et al. (2024). Operational Research: methods and applications. Journal of the Operational Research Society, 75(3), pp. 423–617, 2023. DOI: 10.1080/01605682.2023.2253852 (Open Access)
  4. E. Alper Yıldırım. An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs. Journal of Global Optimization, 82, pp. 1-20, 2022. DOI: 10.1007/s10898-021-01066-3 (Open Access) (2023 Journal of Global Optimization Best Paper Honourable Mention)
  5. Y. Gorkem Gokmen and E. Alper Yıldırım. On standard quadratic programs with exact and inexact doubly nonnegative relaxations. Mathematical Programming, 193, pp. 365-403, 2022. DOI: 10.1007/s10107-020-01611-0 (Open Access)
  6. Jacek Gondzio and E. Alper Yıldırım. Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations. Journal of Global Optimization, 81, pp. 293-321, 2021. DOI: 10.1007/s10898-021-01017-y (Open Access)
  7. Gunes Erdogan and E. Alper Yıldırım. 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
  8. Ali Yesilcimen and E. Alper Yıldırım. 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
  9. E. Alper Yıldırım. 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
  10. Refail Kasimbeyli and E. Alper Yıldırım. Optimality conditions in nonconvex and nonsmooth optimization revisited. Pure and Applied Functional Analysis, 2 (1), pp. 99-109, 2017. Paper
  11. Kagan Gokbayrak and E. Alper Yıldırım. 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
  12. Gizem Sagol and E. Alper Yıldırım. 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
  13. Emre Mengi, E. Alper Yıldırım, 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
  14. Immanuel M. Bomze, Stefan Gollowitzer, and E. Alper Yıldırım. 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 (2015 Journal of Global Optimization Best Paper Award)
  15. Kagan Gokbayrak and E. Alper Yıldırım. 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
  16. Esra Koca and E. Alper Yıldırım. 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
  17. E. Alper Yıldırım. 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
  18. Piyush Kumar and E. Alper Yıldırım. 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
  19. E. Alper Yıldırım. 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
  20. Piyush Kumar and E. Alper Yıldırım. 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
  21. Piyush Kumar and E. Alper Yıldırım. 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
  22. S. Damla Ahipasaoglu and E. Alper Yıldırım. 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
  23. Elizabeth John and E. Alper Yıldırım. 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
  24. E. Alper Yıldırım. Two algorithms for the minimum enclosing ball problem. SIAM Journal on Optimization, 19 (3), pp. 1368-1391, 2008. DOI: 10.1137/070690419
  25. Michael J. Todd and E. Alper Yıldırım. 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
  26. E. Alper Yıldırım 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
  27. E. Alper Yıldırım. 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)
  28. Piyush Kumar and E. Alper Yıldırım. 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
  29. E. Alper Yıldırım. 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
  30. Piyush Kumar, Joseph S. B. Mitchell, and E. Alper Yıldırım. 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))
  31. E. Alper Yıldırım. 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
  32. E. Alper Yıldırım 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
  33. E. Alper Yıldırım 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
  34. E. Alper Yıldırım 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 Yıldırım. 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
Last updated on 5 December 2023.