Search for: All records

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by summation of a smooth, possibly nonconvex function and a convex simple function. The algorithm converts the original problem into a sequence of convex subproblems. Formulating those subproblems requires the evaluation of at most one gradient-value of the original objective and constraint functions. Either exact or approximate subproblems solutions can be computed efficiently in many cases. An important feature of the algorithm is the constraint level parameter. By carefully increasing this level for each subproblem, we provide a simple solution to overcome the challenge of bounding the Lagrangian multipliers and show that the algorithm follows a strictly feasible solution path till convergence to the stationary point. We develop a simple, proximal gradient descent type analysis, showing that the complexity bound of this new algorithm is comparable to gradient descent for the unconstrained setting which is new in the literature. Exploiting this new design and analysis technique, we extend our algorithms to some more challenging constrained optimization problems where (1) the objective is a stochastic or finite-sum function, and (2) structured nonsmooth functions replace smooth components of both objective and constraint functions. Complexity results for these problems also seem to be new in the literature. Finally, our method can also be applied to convex function constrained problems where we show complexities similar to the proximal gradient method.

 

Waste biorefining processes face significant challenges related to the variability of feedstocks. The supply and composition of multiple feedstocks in these processes can be uncertain, making it difficult to achieve economically feasible and sustainable waste valorization for large-scale production. Here, we introduce a reinforcement learning-based framework that aims to control these uncertainties and improve the efficiency of the process. The framework is tested on an anaerobic digestion process and is found to perform better than traditional control strategies. In the short term, it achieves faster target tracking with increased precision and accuracy, while in the long term, it shows adaptive and robust behavior even under additional seasonal supply variability, meeting downstream demand with high probability. This reinforcement learning-based framework offers a promising and scalable solution to address uncertainty issues in real-world biorefining processes. If implemented, this framework could contribute to sustainable waste management practices globally, making waste biorefining processes more economically viable and environmentally friendly.

 

Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an L1 regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the graph structure. Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix. However, it is a challenging task in this case, since the symmetric positive definiteness (SPD) and sparsity of the matrix are not easy to enforce in learned algorithms, and a direct mapping from data to precision matrix may contain many parameters. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization (AM) algorithm as our model inductive bias, and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data.