相关论文: Another source of mesh dependence in topology opti…

Recent progress in LLM-driven algorithm discovery, exemplified by DeepMind's AlphaEvolve, has produced new best-known solutions for a range of hard geometric and combinatorial problems. This raises a natural question: to what extent can…

We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which is an adaptive importance technique useful to sample multimodal target distributions. The importance function is based on the weights (namely the…

We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…

A factored Nonlinear Program (Factored-NLP) explicitly models the dependencies between a set of continuous variables and nonlinear constraints, providing an expressive formulation for relevant robotics problems such as manipulation planning…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…

Neural networks (NN) perform well in diverse tasks, but sometimes produce nonsensical results to humans. Most NN models "solely" learn from (input, output) pairs, occasionally conflicting with human knowledge. Many studies indicate…

This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…

In this paper, we focus on a class of constrained nonlinear optimization problems (NLP), where some of its equality constraints define a closed embedded submanifold $\mathcal{M}$ in $\mathbb{R}^n$. Although NLP can be solved directly by…

This paper surveys studies on the use of neural networks for optimization in the training-data-free setting. Specifically, we examine the dataless application of neural network architectures in optimization by re-parameterizing problems…

The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a…

Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…

Topology optimization is a widely used design method that produces optimized material distributions for prescribed objectives and constraints through well-established numerical algorithms. Throughout the workflow, engineers make a series of…

In decentralized optimization, nodes cooperate to minimize an overall objective function that is the sum (or average) of per-node private objective functions. Algorithms interleave local computations with communication among all or a subset…

The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…

Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…