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:我们提出了解决限制优化问题的一级方法。该方法来自我们以前的工作,即根据单值分解而修改的搜索方向方法。在这项工作中,我们将其计算框架简化为“渐渐下降的近似方法”(GDAM),即搜索方向的计算使用负和正常目标和约束梯度的线性组合计算。我们对方法的全球趋同提供了基本的理论保证。这项工作侧重于GDAM的算法和应用。我们提出了调整梯度下降方法共同战略的计算算法。我们用两种工程应用,即形状优化和传感器网络本地化来展示该方法的潜力。在实际实施时,GDAM在解决考虑的大型和具有挑战性的优化问题时,具有很强的竞争力。