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An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We study optimization problems where the objective function is modeled through feedforward neural networks with rectified linear unit (ReLU) activation. Recent literature has explored the use of a single neural network to model either…
Constrained Reinforcement Learning has been employed to enforce safety constraints on policy through the use of expected cost constraints. The key challenge is in handling expected cost accumulated using the policy and not just in a single…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
The design of deterministic filters can be cast as a problem of minimizing an associated cost function for an optimal control problem. Employing the min-plus linearity property of the dynamic programming operator (associated with the…
Although well-established in general reinforcement learning (RL), value-based methods are rarely explored in constrained RL (CRL) for their incapability of finding policies that can randomize among multiple actions. To apply value-based…
We study the problem of multi-class classification under system-level constraints expressible as linear functionals over randomized classifiers. We propose a post-processing approach that adjusts a given base classifier to satisfy general…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant…
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
Convolutional Neural Networks (CNN) have been found to have great potential in optical flow problems thanks to an abundance of data available for training a deep network. The displacement estimation step in UltraSound Elastography (USE) can…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Safe Reinforcement Learning (RL) often faces significant issues such as constraint violations and instability, necessitating the use of constrained policy optimization, which seeks optimal policies while ensuring adherence to specific…
The motivation for this work stems from the problem of scheduling requests for flow at supply points along an automated network of open-water channels. The off-take flows are rigid-profile inputs to the system dynamics. In particular, the…
In this article, we propose a data-enabled economic predictive control method for a class of nonlinear systems, which aims to optimize the economic operational performance while handling hard constraints on the system outputs. Two lifting…
Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches…
This study investigates imposing hard inequality constraints on the outputs of convolutional neural networks (CNN) during training. Several recent works showed that the theoretical and practical advantages of Lagrangian optimization over…