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Recent contributions to linear semi-infinite optimization: an update

Author

Listed:
  • M. A. Goberna

    (University of Alicante)

  • M. A. López

    (University of Alicante
    Federation University of Australia)

Abstract

This paper reviews the state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization, presents some numerical approaches to this type of problems, and describes a selection of recent applications in a variety of fields. Extensions to related optimization areas, as convex semi-infinite optimization, linear infinite optimization, and multi-objective linear semi-infinite optimization, are also commented.

Suggested Citation

  • M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    • Handle: RePEc:spr:annopr:v:271:y:2018:i:1:d:10.1007_s10479-018-2987-8
    DOI: 10.1007/s10479-018-2987-8
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    1. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    2. A. Vaz & Edite Fernandes & M. Gomes, 2003. "A sequential quadratic programming with a dual parametrization approach to nonlinear semi-infinite programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 109-130, June.
    3. İ. Altınel & Bora Çekyay & Orhan Feyzioğlu & M. Keskin & Süleyman Özekici, 2011. "Mission-Based Component Testing for Series Systems," Annals of Operations Research, Springer, vol. 186(1), pages 1-22, June.
    4. M. J. Cánovas & R. Henrion & M. A. López & J. Parra, 2016. "Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 925-952, June.
    5. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2017. "No-arbitrage bounds for the forward smile given marginals," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1243-1256, August.
    6. Xiaojiao Tong & Soon-Yi Wu & Renjun Zhou, 2010. "New approach for the nonlinear programming with transient stability constraints arising from power systems," Computational Optimization and Applications, Springer, vol. 45(3), pages 495-520, April.
    7. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
    8. F. Leibfritz & J. Maruhn, 2009. "A successive SDP-NSDP approach to a robust optimization problem in finance," Computational Optimization and Applications, Springer, vol. 44(3), pages 443-466, December.
    9. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    10. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    11. M. D. Fajardo & M. A. López, 1999. "Locally Farkas–Minkowski Systems in Convex Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 313-335, November.
    12. M. J. Cánovas & A. Hantoute & J. Parra & F. J. Toledo, 2014. "Calmness of the Argmin Mapping in Linear Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 111-126, January.
    13. İ. Altinel & Bora Çekyay & Orhan Feyzio[gtilde]lu & M. Keskin & Süleyman Özekici, 2013. "The design of mission-based component test plans for series connection of subsystems," IISE Transactions, Taylor & Francis Journals, vol. 45(11), pages 1202-1220.
    14. Feyzioglu, Orhan & Altinel, I. Kuban & Ozekici, Suleyman, 2008. "Optimum component test plans for phased-mission systems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 255-265, February.
    15. Goberna, M.A. & Gomez, S. & Guerra, F. & Todorov, M.I., 2007. "Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1069-1085, September.
    16. Edward J. Anderson & Miguel A. Goberna & Marco A. López, 2001. "Simplex-Like Trajectories on Quasi-Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 147-162, February.
    17. A. Charnes & W. W. Cooper & K. O. Kortanek, 1969. "On the theory of semi‐infinite programming and a generalization of the kuhn‐tucker saddle point theorem for arbitrary convex functions," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 16(1), pages 41-52, March.
    18. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    19. M. A. Goberna & T. Terlaky & M. I. Todorov, 2010. "Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 14-26, February.
    20. Alfred Auslender & Miguel A. Goberna & Marco A. López, 2009. "Penalty and Smoothing Methods for Convex Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 303-319, May.
    21. A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
    22. Robert J. Vanderbei, 1995. "Affine-Scaling Trajectories Associated with a Semi-Infinite Linear Program," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 163-174, February.
    23. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    24. Diego Klabjan & Daniel Adelman, 2007. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 528-550, August.
    25. Audy, Jean-François & D’Amours, Sophie & Rönnqvist, Mikael, 2012. "An empirical study on coalition formation and cost/savings allocation," International Journal of Production Economics, Elsevier, vol. 136(1), pages 13-27.
    26. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.
    27. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
    28. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    29. Emre Yamangil & İ. Altınel & Bora Çekyay & Orhan Feyziog[gtilde]lu & Süleyman Özekici, 2011. "Design of optimum component test plans in the demonstration of diverse system performance measures," IISE Transactions, Taylor & Francis Journals, vol. 43(7), pages 535-546.
    30. Zhu, Y. & Huang, G.H. & Li, Y.P. & He, L. & Zhang, X.X., 2011. "An interval full-infinite mixed-integer programming method for planning municipal energy systems - A case study of Beijing," Applied Energy, Elsevier, vol. 88(8), pages 2846-2862, August.
    31. Levent Tunçel & Michael J. Todd, 1996. "Asymptotic Behavior of Interior-Point Methods: A View From Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 354-381, May.
    32. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    33. Goberna, M.A. & Guerra-Vazquez, F. & Todorov, M.I., 2016. "Constraint qualifications in convex vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 249(1), pages 32-40.
    34. Amitabh Basu & Kipp Martin & Christopher Thomas Ryan, 2015. "Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 146-170, February.
    35. Qinghong Zhang, 2017. "Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier–Motzkin Elimination Approach," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 702-717, December.
    36. Archis Ghate & Dushyant Sharma & Robert L. Smith, 2010. "A Shadow Simplex Method for Infinite Linear Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 865-877, August.
    37. A. Charnes & W. W. Cooper & K. Kortanek, 1965. "On Representations of Semi-Infinite Programs which Have No Duality Gaps," Management Science, INFORMS, vol. 12(1), pages 113-121, September.
    38. Goberna, M.A. & Guerra-Vazquez, F. & Todorov, M.I., 2013. "Constraint qualifications in linear vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 227(1), pages 12-21.
    39. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    40. E. González-Gutiérrez & L. Hernández Rebollar & Maxim Todorov, 2012. "Relaxation methods for solving linear inequality systems: converging results," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 426-436, July.
    41. S. Å. Gustafson & K. O. Kortanek, 1973. "Numerical treatment of a class of semi‐infinite programming problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 477-504, September.
    42. R. J. Duffin & L. A. Karlovitz, 1965. "An Infinite Linear Program with a Duality Gap," Management Science, INFORMS, vol. 12(1), pages 122-134, September.
    43. Faizan Ahmed & Mirjam Dür & Georg Still, 2013. "Copositive Programming via Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 322-340, November.
    44. Nichalin Suakkaphong & Moshe Dror, 2011. "Managing decentralized inventory and transshipment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 480-506, December.
    45. J. Lasserre, 2012. "An algorithm for semi-infinite polynomial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 119-129, April.
    46. Javier Pena & Juan Vera & Luis Zuluaga, 2010. "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 819-827.
    47. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, June.
    48. M. A. Goberna & M. A. López, 2017. "Recent contributions to linear semi-infinite optimization," 4OR, Springer, vol. 15(3), pages 221-264, September.
    49. A. Charnes & W. W. Cooper & K. Kortanek, 1963. "Duality in Semi-Infinite Programs and Some Works of Haar and Carathéodory," Management Science, INFORMS, vol. 9(2), pages 209-228, January.
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