A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most important element of the construction is the presence of the Carleman Weight Function in a weighted Tikhonov-like functional. This functional is strictly convex on a certain bounded set in a Hilbert space, and the diameter of this set is an arbitrary positive number. The global convergence of the gradient projection method is established. Computational results demonstrate a good performance of the numerical method for noisy data.

中文翻译：

---

一维单曲双曲系数反问题的凸性

提出了一维双曲型PDE系数反问题凸化数值方法的一种形式。此问题的数据由单个测量事件生成。该方法全局收敛。构造中最重要的元素是在类似Tikhonov的加权函数中存在Carleman加权函数。该函数在希尔伯特空间中的某个有界集合上是严格凸的，并且该集合的直径是任意正数。建立了梯度投影方法的全局收敛性。计算结果证明了数值方法对噪声数据的良好性能。