论文标题
关于二进制信任区域最陡峭下降的收敛
On Convergence of Binary Trust-Region Steepest Descent
论文作者
论文摘要
二进制信任区域最陡峭的下降（BTR）和组合积分近似（CIA）是最近研究的两种方法，用于解决分布式二进制二进制/离散变量的优化问题（控制函数）。通过施加与CIA收敛理论相似的紧凑性假设，我们显示了BTR的收敛结果的改善。作为推论，我们得出的结论是，BTR还构成了连续放松的下降算法，其迭代量微弱地收敛 - $^*$与后者的固定点。我们提供验证我们发现的计算结果。此外，我们观察到BTR的正则作用，我们通过CIA和BTR的杂交进行探索。
Binary trust-region steepest descent (BTR) and combinatorial integral approximation (CIA) are two recently investigated approaches for the solution of optimization problems with distributed binary-/discrete-valued variables (control functions). We show improved convergence results for BTR by imposing a compactness assumption that is similar to the convergence theory of CIA. As a corollary we conclude that BTR also constitutes a descent algorithm on the continuous relaxation and its iterates converge weakly-$^*$ to stationary points of the latter. We provide computational results that validate our findings. In addition, we observe a regularizing effect of BTR, which we explore by means of a hybridization of CIA and BTR.
