|
|
基数约束优化问题的内罚函数法
|
Abstract:
基数约束优化问题是一类重要的优化问题，这类问题在很多领域都有着广泛的应用。由于其具有较难处理的基数约束，所以对基数约束优化问题的算法研究较少。本文将介绍基数约束优化问题的内罚函数法，并证明了该算法产生点列收敛到AM-稳定点。进一步证明在AM-正则性条件下，可以得到基数约束优化问题的M-稳定点。
The cardinality-constrained optimization problems are an important class of optimization problems which have been applied in many fields. Due to the special structure of the cardinality constraints, there are few researches on the algorithm of cardinality-constraint optimization problems. We in-troduce an interior penalty algorithm for cardinality-constrained optimization problems and prove that the algorithm reaches an approximate Mordukhovich stationary. Furthermore, under the AM-regularity condition, we can obtain the Mordukhovich stationary of cardinality-constrained op-timization problems.
| [1] | Burdakov, O.P., Kanzow, C. and Schwartz, A. (2016) Mathematical Programs with Cardinality Constraints: Reformula-tion by Complementarity-Type Conditions and a Regularization Method. SIAM Journal on Optimization, 26, 397-425.
https://doi.org/10.1137/140978077 |
| [2] | Bertsimas, D. and Shioda, R. (2009) Algorithm for Cardinali-ty-Constrained Quadratic Optimization. Computational Optimization and Applications, 43, 1-22. https://doi.org/10.1007/s10589-007-9126-9 |
| [3] | Dong, H., Ahn, M. and Pang, J.S. (2019) Structural Properties of Affine Sparsity Constraints. Mathematical Programming, 176, 95-135. https://doi.org/10.1007/s10107-018-1283-3 |
| [4] | Krulikovski, M.H.E., Ribeiro, A.A. and Sachine, M. (2021) On the Weak Stationarity Conditions for Mathematical Programs with Cardinality Constraints: A Unified Approach. Applied Mathematics & Optimization, 84, 3451-3473.
https://doi.org/10.1007/s00245-021-09752-0 |
| [5] | Kanzow, C., Raharja, B.A. and Schwartz, A. (2021) An Aug-mented Lagrangian Method for Cardinality-Constrained Optimization Problems. Journal of Optimization Theory and Ap-plications, 189, 793-813.
https://doi.org/10.1007/s10957-021-01854-7 |
| [6] | Kanzow, C., Raharja, A.B. and Schwartz, A. (2021) Sequential Optimality Conditions for Cardinality-Constrained Optimization Problems with Applications. Computational Optimiza-tion and Applications, 80, 185-211.
https://doi.org/10.1007/s10589-021-00298-z |
| [7] | Xue, M.L. and Pang, L.P. (2022) A Strong Sequential Optimality Condition for Cardinality-Constrained Optimization Problems. Numerical Algorithms, 92, 1875-1904. https://doi.org/10.1007/s11075-022-01371-2 |
| [8] | Ribeiro, A.A., Sachine, M. and Krulikovski, E.H.M. (2022) A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints. Journal of Optimization Theory and Applications, 192, 1067-1083.
https://doi.org/10.1007/s10957-022-02007-0 |
| [9] | Rockafellar, R.T. and Wets, J.B. (2009) Variational Analysis. Springer-Verlag, Berlin. |
| [10] | Leyffer, S., López-Calva, G. and Nocedal, J. (2006) Interior Methods for Mathematical Programs with Complementarity Constraints. SIAM Journal on Optimization, 17, 52-77. https://doi.org/10.1137/040621065 |
| [11] | Forsgren, A., Gill, P.E. and Wright, M.H. (2002) Interior Methods for Nonlinear Optimization. SIAM Review, 44, 525-597. https://doi.org/10.1137/S0036144502414942 |
