相关论文: Sensitivity Analysis for Piecewise-Affine Approxim…

We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, including complexity, regularity, and algorithms. Specifically, we…

Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…

The control of large buildings encounters challenges in computational efficiency due to their size and nonlinear components. To address these issues, this paper proposes a Piecewise Affine (PWA)-based distributed scheme for Model Predictive…

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…

Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…

This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…

Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and trustworthiness while also enhancing inference accuracy. Despite the nonlinear nature of most real-world tasks, the majority of existing…

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning…

Model predictive control problems for constrained hybrid systems are usually cast as mixed-integer optimization problems (MIP). However, commercial MIP solvers are designed to run on desktop computing platforms and are not suited for…

As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs)…

A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a.\ MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as…

We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the…

Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a…

We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear…

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…

In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…