Related papers: NC2C: Automated Convexification of Generic Non-Con…

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…

Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support…

Learning-to-optimize (L2O) is an emerging research area in large-scale optimization with applications in data science. Recently, researchers have proposed a novel L2O framework called learned mirror descent (LMD), based on the classical…

Motivated by Smart Manufacturing and Industry 4.0, we introduce a framework for synthesizing Abstraction-Based Controller Design (ABCD) for reach-avoid problems from Natural Language (NL) specifications using Large Language Models (LLMs). A…

Autonomous control systems face significant challenges in performing complex tasks in the presence of latent risks. To address this, we propose an integrated framework that combines Large Language Models (LLMs), numerical optimization, and…

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…

Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…

Large Language Model (LLM)-based optimization has recently shown promise for autonomous problem solving, yet most approaches still cast LLMs as passive constraint checkers rather than proactive strategy designers, limiting their…

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 study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers,…

Large language models (LLMs) have greatly accelerated the automation of algorithm generation and optimization. However, current methods such as EoH and FunSearch mainly rely on predefined templates and expert-specified functions that focus…

Visual reasoning is dominated by end-to-end neural networks scaled to billions of model parameters and training examples. However, even the largest models struggle with compositional reasoning, generalization, fine-grained spatial and…

Congestion control is a fundamental component of Internet infrastructure, and researchers have dedicated considerable effort to developing improved congestion control algorithms. However, despite extensive study, existing algorithms…

Reasoning is the fundamental capability of large language models (LLMs). Due to the rapid progress of LLMs, there are two main issues of current benchmarks: i) these benchmarks can be crushed in a short time (less than 1 year), and ii)…

Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on…