IPM-LSTM: A Learning-Based Interior Point Method for Solving Nonlinear Programs

Xi Gao, Jinxin Xiong, Akang Wang, Qihong Duan, Jiang Xue, Qingjiang Shi

Keywords: learning to optimize, interior point method, nonlinear constrained programs

Abstract: Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM). The most computationally expensive procedure in IPMs is to solve systems of linear equations via matrix factorization. Recently, machine learning techniques have been adopted to expedite classic optimization algorithms. In this work, we propose using Long Short-Term Memory (LSTM) neural networks to approximate the solution of linear systems and integrate this approximating step into an IPM. The resulting approximate NLP solution is then utilized to warm-start an interior point solver. Experiments on various types of NLPs, including Quadratic Programs and Quadratically Constrained Quadratic Programs, show that our approach can significantly accelerate NLP solving, reducing iterations by up to 60% and solution time by up to 70% compared to the default solver.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 18597