Accelerated Algorithms for a Class of Optimization Problems with Constraints
Accelerated Algorithms for a Class of Optimization Problems with Constraints
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DOI：
10.1109/cdc51059.2022.9993120
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Anjali Parashar;P. Srivastava;A. Annaswamy
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文献类型：
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作者：
Anjali Parashar;P. Srivastava;A. Annaswamy
提出了一种基于高阶调谐器(HT)的约束优化加速求解框架。我们的方法是基于将原始的约束问题重新表示为损失函数的无约束优化。我们从凸优化问题入手，确定了损失函数是凸的条件。基于损失函数即使在原优化问题不是凸的情况下也可能是凸的这一观点，我们将方法扩展到一类非凸优化问题。与最先进的基于梯度的方法相比，HT和这种方法的结合使用使我们能够获得更好的收敛速度。此外，对于等式约束优化问题，该方法确保了状态在整个进化过程中保持可行，而不考虑原始问题的凸性。
This paper presents a framework to solve con strained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization of a loss function. We start with convex optimization problems and identify the conditions under which the loss function is convex. Building on the insight that the loss function could be convex even if the original optimization problem is not, we extend our approach to a class of nonconvex optimization problems. The use of a HT together with this approach enables us to achieve a convergence rate better than state-of-the-art gradient-based methods. Moreover, for equality-constrained optimization problems, the proposed method ensures that the state remains feasible throughout the evolution, regardless of the convexity of the original problem.