Automatic robust convex programming. (English) Zbl 1242.90289
Summary: This paper presents the robust optimization framework in the modelling language YALMIP, which carries out robust modelling and uncertainty elimination automatically and allows the user to concentrate on the high-level model. While introducing the software package, a brief summary of robust optimization is given, as well as some comments on modelling and tractability of complex convex uncertain optimization problems.
MSC:
| 90C47 | Minimax problems in mathematical programming |
Software:
YALMIPReferences:
| [1] | DOI: 10.1287/moor.23.4.769 · Zbl 0977.90052 · doi:10.1287/moor.23.4.769 |
| [2] | DOI: 10.1016/S0167-6377(99)00016-4 · Zbl 0941.90053 · doi:10.1016/S0167-6377(99)00016-4 |
| [3] | DOI: 10.1007/s101070100286 · Zbl 1007.90047 · doi:10.1007/s101070100286 |
| [4] | Boyd S., Convex Optimization (2004) |
| [5] | DOI: 10.1137/1.9781611970777 · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [6] | DOI: 10.1007/s10107-003-0499-y · Zbl 1177.90317 · doi:10.1007/s10107-003-0499-y |
| [7] | DOI: 10.1137/S1052623496305717 · Zbl 0960.93007 · doi:10.1137/S1052623496305717 |
| [8] | DOI: 10.1287/opre.24.4.783 · Zbl 0335.90035 · doi:10.1287/opre.24.4.783 |
| [9] | DOI: 10.1007/BF01585511 · Zbl 0326.90049 · doi:10.1007/BF01585511 |
| [10] | DOI: 10.1007/978-1-84800-155-8_7 · Zbl 1205.90223 · doi:10.1007/978-1-84800-155-8_7 |
| [11] | Hardy G., Inequalities, 2. ed. (1952) |
| [12] | Lasserre J.-B., Optimization Series, in: Moments, Positive Polynomials and Their Applications (2009) |
| [13] | Löfberg, J. Approximations of Closed-loop MPC. Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii. pp.1438–1442. |
| [14] | Löfberg, J. YALMIP: A Toolbox for Modeling and Optimization in MATLAB. Proceedings of the 13th IEEE International Symposium on Computer Aided Control System Design. Taipei, Taiwan. |
| [15] | Löfberg, J. Modeling and Solving Uncertain Optimization Problems in YALMIP. Proceedings of the 17th IFAC World Congress on Automatic Control. Seoul, South Korea. |
| [16] | DOI: 10.1109/TAC.2009.2017144 · Zbl 1367.90002 · doi:10.1109/TAC.2009.2017144 |
| [17] | DOI: 10.1137/0607052 · Zbl 0589.68033 · doi:10.1137/0607052 |
| [18] | DOI: 10.1007/s10107-003-0387-5 · Zbl 1043.14018 · doi:10.1007/s10107-003-0387-5 |
| [19] | Prekopa A., Stochastic Programming, Mathematics and its Applications (1995) |
| [20] | DOI: 10.1137/S0895479803430953 · Zbl 1122.93063 · doi:10.1137/S0895479803430953 |
| [21] | M. Sim,Robust optimization, Ph.D. thesis, Massachusetts Institute of Technology, 2004 |
| [22] | Goh J., Oper. Res. |
| [23] | DOI: 10.1287/opre.21.5.1154 · Zbl 0266.90046 · doi:10.1287/opre.21.5.1154 |
| [24] | DOI: 10.1287/opre.22.4.892 · Zbl 0287.90015 · doi:10.1287/opre.22.4.892 |
| [25] | Zhou, K., Doyle, J. C. and Glover, K. 1995. ”Robust and Optimal Control”. Upper Saddle River, NJ: Prentice Hall. · Zbl 0999.49500 |
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