- 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 so as to cut back the duality hole. We examine the circumstances wherein blended integer convex optimization issues have a precise penalty illustration utilizing sharp augmenting capabilities (norms as augmenting penalty capabilities). We current a generalizable constructive proof approach for proving existence of tangible penalty representations for blended integer convex applications below particular situations utilizing the related worth capabilities. This generalizes the current outcomes for MILP (Feizollahi, Ahmed and Solar, 2017) and MIQP (Gu, Ahmed and Dey 2020) while additionally offering an alternate 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 methods is eternal challenges for the elemental analysis in science and engineering. Machine studying has exhibited nice success to study and predict dynamical methods from knowledge. Nonetheless, the elemental challenges nonetheless exist: discovering the precise governing equations from extremely noisy knowledge. 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. Particularly, we first formulate the issue right into a blended integer optimization mannequin. The discrete optimization nature of the mannequin results in actual variable choice via cardinality constraint, and hereby highly effective functionality of tangible discovery of governing equations from noisy knowledge. Such functionality is additional enhanced by incorporating compressive sensing and regularization strategies for extremely noisy knowledge and high-dimensional issues. The case research on classical dynamical methods have proven that CS-MIO can uncover the precise governing equations from large-noise knowledge, 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 by the chaotic Lorenz 96 system.
