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Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…
This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This…
Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet…
Recent research has demonstrated the effectiveness of large language models (LLMs) in solving combinatorial optimization problems (COPs) by representing tasks and instances in natural language. However, purely language-based approaches…
Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, we extend the analysis of the orthogonal greedy algorithm…
We propose a non-convex variational model for the super-resolution of Optical Coherence Tomography (OCT) images of the murine eye, by enforcing sparsity with respect to suitable dictionaries learnt from high-resolution OCT data. The…
Multi-objective optimization problems (MOPs) are ubiquitous in real-world applications, presenting a complex challenge of balancing multiple conflicting objectives. Traditional evolutionary algorithms (EAs), though effective, often rely on…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Program synthesis is an umbrella term for generating programs and logical formulae from specifications. With the remarkable performance improvements that GPUs enable for deep learning, a natural question arose: can we also implement a…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
GPUs have become essential in modern high performance computing, but programming them correctly remains a significant challenge. This difficulty arises from subtle concurrency bugs that result from the explicit management of synchronization…
In this work, we propose GLOV, which enables Large Language Models (LLMs) to act as implicit optimizers for Vision-Language Models (VLMs) to enhance downstream vision tasks. GLOV prompts an LLM with the downstream task description, querying…
Autonomous driving perception faces significant challenges due to occlusions and incomplete scene data in the environment. To overcome these issues, the task of semantic occupancy prediction (SOP) is proposed, which aims to jointly infer…
Advances in machine learning technology have enabled real-time extraction of semantic information in signals which can revolutionize signal processing techniques and improve their performance significantly for the next generation of…
The rapid progress of artificial intelligence increasingly relies on efficient integrated circuit (IC) design. Recent studies have explored the use of large language models (LLMs) for generating Register Transfer Level (RTL) code, but…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
In recent years, diffusion models have become the most popular and powerful methods in the field of image synthesis, even rivaling human artists in artistic creativity. However, the key issue currently limiting the application of diffusion…
Optimizing GPU kernels with LLM agents is an iterative process over a large design space. Every candidate must be generated, compiled, validated, and profiled, so fewer trials will save both runtime and cost. We make two key observations.…