Bilinear Matrix Inequality

Bilinear matrix inequalities (BMIs) are a class of mathematical problems arising in various fields, primarily focusing on optimizing systems described by bilinear relationships between matrices. Current research emphasizes developing efficient algorithms to solve BMIs, often employing techniques like variable substitution, convex relaxations, and iterative methods based on linear matrix inequalities (LMIs) to handle the inherent non-convexity. These methods find applications in diverse areas, including robotics (grasp force optimization), machine learning (class incremental learning, knowledge graph embedding), and signal processing (digital filtering), improving the performance and robustness of existing systems. The development of novel algorithms and their application to real-world problems continues to be a significant focus.