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This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
Recently, a Riemannian proximal Newton method has been developed for optimizing problems in the form of $\min_{x\in\mathcal{M}} f(x) + \mu \|x\|_1$, where $\mathcal{M}$ is a compact embedded submanifold and $f(x)$ is smooth. Although this…
In this paper, we propose two second-order methods for solving the \(\ell_1\)-regularized composite optimization problem, which are developed based on two distinct definitions of approximate second-order stationary points. We introduce a…
Moment-closure approximations are an important tool in the analysis of the dynamics on both static and adaptive networks. Here, we provide a broad survey over different approximation schemes by applying each of them to the adaptive voter…
The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical…
In recent years, the proximal gradient method and its variants have been generalized to Riemannian manifolds for solving optimization problems with an additively separable structure, i.e., $f + h$, where $f$ is continuously differentiable,…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…
We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…
Background: Advanced adaptive randomised clinical trials are increasingly used. Compared to their conventional counterparts, their flexibility may make them more efficient, increase the probability of obtaining conclusive results without…
We consider the problem of uniformity testing of Lipschitz continuous distributions with bounded support. The alternative hypothesis is a composite set of Lipschitz continuous distributions that are at least $\varepsilon$ away in $\ell_1$…
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis and…
Affinity propagation clustering (AP) has two limitations: it is hard to know what value of parameter 'preference' can yield an optimal clustering solution, and oscillations cannot be eliminated automatically if occur. The adaptive AP method…