|
|
随机对称锥规划问题的一阶最优性条件的相容性分析
|
Abstract:
随机对称锥规划问题是一类应用十分广泛的问题，在工程设计、通讯、控制等实际领域有着重要的应用。随着优化问题不断的深入研究和对称锥规划理论的完善，许多很难甚至不能解决的问题，都可以转化为对称锥优化模型。因此，关于随机对称锥规划问题的研究有着重要的价值。对于随机对称锥规划问题的研究，本文采用了基于样本的近似方法，通常需要考虑样本均值近似问题的相容性，本文将对随机对称锥规划问题的样本均值近似问题的最优值和一阶最优性条件的相容性进行分析。
Stochastic symmetric cone programming problem is a very wide range of problems, which has im-portant applications in engineering design, communication, control and other practical fields. With the continuous in-depth study of optimization problems and the improvement of symmetric cone programming theory, many difficult or even unsolvable problems can be transformed into symmet-ric cone optimization model. Therefore, the research on stochastic symmetric cone programming is of great value. For the research of stochastic symmetric cone programming, this paper adopts the sample based approximation method, which usually needs to consider the compatibility of the sample mean approximation problem. This paper will analyze the compatibility of the optimal val-ue and the first-order optimality condition of the sample mean approximation problem of stochastic symmetric cone programming.
| [1] | Ferguson, A.R. and Dantzig, G.B. (1956) The Allocation of Aircraft to Routes—An Example of Linear Programming under Uncertain Demand. Management Science, 3, 45-73. https://doi.org/10.1287/mnsc.3.1.45 |
| [2] | Dai, L., Chen, C.H. and Birge, J.R. (2000) Convergence Properties of Two-Stage Stochastic Programming. Journal of Optimization Theory & Applications, 106, 489-509. https://doi.org/10.1023/A:1004649211111 |
| [3] | Faybusovich, L. (1997) Eu-clidean Jordan Algebras and Interior-Point Algorithms. Positivity, 1, 331-357.
https://doi.org/10.1023/A:1009701824047 |
| [4] | Schmieta, S.H. and Alizadch, F. (2001) Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones. Mathematics of Operations Research, 26, 543-564.
https://doi.org/10.1287/moor.26.3.543.10582 |
| [5] | Henry, W., Romesh, S. and Lieven, V. (2000) Handbook of Semidefinite Programming: Theory, Algorithms, and Applications Printed in the United States of America. Kluwer Aca-demic Publishers, Totnes. |
| [6] | Klerk, E.D. (2002) Aspects of Semidefinite Programming. Kluwer Academic Publishers, Totnes. |
| [7] | Bastin, F., Cirillo, C. and Toint, P.L. (2006) Convergence Theory for Nonconvex Stochastic Programming with an Application to Mixed Logit. Mathematical Programming, 108, 207-234. https://doi.org/10.1007/s10107-006-0708-6 |
| [8] | Bastin, F., Cirillo, C. and Toint, P.L. (2006) An Adaptive Mon-tecarlo Algorithm for Computing Mixed Logit Estimators. Computational Management Science, 3, 55-79. https://doi.org/10.1007/s10287-005-0044-y |
| [9] | Faraut, J. and Korányi, A. (1994) Analysis on Symmetric Cones. Clarendon Press, Oxford. |
| [10] | Shapiro, A. (2000) Stochastic Programming by Monte Carlo Simulation Methods. SPEPS, SIAM.
https://doi.org/10.1137/1.9780898718751 |
| [11] | Shapiro, A., Dentcheva, D. and Ruszczyński, A. (2009) Lectures on Stochastic Programming: Modeling and Theory. SIAM, Phladelphia. |
