We present a first-order method for solving constrained optimization problems. The method is derived from our previous work, a modified search direction method inspired by singular value decomposition. In this work, we simplify its computational framework to a ``gradient descent akin'' method (GDAM), i.e., the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.

翻译：摘要：我们提出了一种用于求解约束优化问题的一阶方法。该方法源于我们先前的工作，即一种受奇异值分解启发的修正搜索方向法。在本研究中，我们将其计算框架简化为一种“类梯度下降”方法（GDAM），即搜索方向由目标函数与约束函数的负梯度及其归一化方向的线性组合计算得出。我们给出了该方法全局收敛性的基本理论保证。本工作重点聚焦于GDAM的算法与应用。我们提出了适应梯度下降法常用策略的计算算法，并通过两个工程应用——形状优化与传感器网络定位——展示了该方法的潜力。在实际实现中，GDAM在求解所考虑的大型且具有挑战性的优化问题时表现出鲁棒性并极具竞争力。