- Exact augmented Lagrangian duality for blended integer convex optimization
Authors: Avinash Bhardwaj, Vishnu Narayanan, Abhishek Pathapati
Abstract: Augmented Lagrangian twin augments the classical Lagrangian twin with a non-negative non-linear penalty carry out of the violation of the relaxed/dualized constraints in order to chop again the duality gap. We look at the circumstances whereby blended integer convex optimization points have a exact penalty illustration using sharp augmenting capabilities (norms as augmenting penalty capabilities). We present a generalizable constructive proof method for proving existence of tangible penalty representations for blended integer convex purposes under explicit conditions using the associated price capabilities. This generalizes the present outcomes for MILP (Feizollahi, Ahmed and Photo voltaic, 2017) and MIQP (Gu, Ahmed and Dey 2020) whereas moreover providing an alternate proof for the aforementioned along with quantification of the finite penalty parameter in these circumstances.
2. Compressive-sensing-assisted blended integer optimization for dynamical system discovery with extraordinarily noisy dataAuthors: Zhongshun Shi, Hang Ma, Hoang Tran, Guannan Zhang
- Abstract: The identification of governing equations for dynamical strategies is everlasting challenges for the basic evaluation in science and engineering. Machine learning has exhibited good success to review and predict dynamical strategies from information. Nonetheless, the basic challenges nonetheless exist: discovering the exact governing equations from extraordinarily noisy information. In present work, we propose a compressive sensing-assisted blended integer optimization (CS-MIO) method to make a step forward from a up to date discrete optimization lens. Significantly, we first formulate the difficulty proper right into a blended integer optimization model. The discrete optimization nature of the model leads to precise variable selection through cardinality constraint, and hereby extremely efficient performance of tangible discovery of governing equations from noisy information. Such performance is extra enhanced by incorporating compressive sensing and regularization methods for terribly noisy information and high-dimensional points. The case analysis on classical dynamical strategies have confirmed that CS-MIO can uncover the exact governing equations from large-noise information, with as a lot as two orders of magnitude greater noise evaluating with state-of-the-art method. We moreover current its effectiveness for high-dimensional dynamical system identification by the chaotic Lorenz 96 system.
