- Precise augmented Lagrangian duality for blended integer convex optimization
Authors: Avinash Bhardwaj, Vishnu Narayanan, Abhishek Pathapati
Summary: Augmented Lagrangian twin augments the classical Lagrangian twin with a non-negative non-linear penalty perform of the violation of the relaxed/dualized constraints with a purpose to scale back the duality hole. We examine the circumstances through which blended integer convex optimization issues have a precise penalty illustration utilizing sharp augmenting features (norms as augmenting penalty features). We current a generalizable constructive proof method for proving existence of actual penalty representations for blended integer convex applications underneath particular circumstances utilizing the related worth features. This generalizes the current outcomes for MILP (Feizollahi, Ahmed and Solar, 2017) and MIQP (Gu, Ahmed and Dey 2020) while additionally offering another proof for the aforementioned together with quantification of the finite penalty parameter in these circumstances.
2. Compressive-sensing-assisted blended integer optimization for dynamical system discovery with extremely noisy dataAuthors: Zhongshun Shi, Hang Ma, Hoang Tran, Guannan Zhang
- Summary: The identification of governing equations for dynamical techniques is eternal challenges for the elemental analysis in science and engineering. Machine studying has exhibited nice success to be taught and predict dynamical techniques from information. Nonetheless, the elemental challenges nonetheless exist: discovering the precise governing equations from extremely noisy information. In current work, we suggest a compressive sensing-assisted blended integer optimization (CS-MIO) technique to make a step ahead from a contemporary discrete optimization lens. Specifically, we first formulate the issue right into a blended integer optimization mannequin. The discrete optimization nature of the mannequin results in precise variable choice by the use of cardinality constraint, and hereby highly effective functionality of actual discovery of governing equations from noisy information. Such functionality is additional enhanced by incorporating compressive sensing and regularization methods for extremely noisy information and high-dimensional issues. The case research on classical dynamical techniques have proven that CS-MIO can uncover the precise governing equations from large-noise information, with as much as two orders of magnitude bigger noise evaluating with state-of-the-art technique. We additionally present its effectiveness for high-dimensional dynamical system identification via the chaotic Lorenz 96 system.
