相关论文: NC2C: Automated Convexification of Generic Non-Con…

This paper develops a unified nonconvex optimization framework for the design of group-sparse feedback controllers in infinite-horizon linear-quadratic (LQ) problems. We address two prominent extensions of the classical LQ problem: the…

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…

Self-correction of large language models (LLMs) emerges as a critical component for enhancing their reasoning performance. Although various self-correction methods have been proposed, a comprehensive evaluation of these methods remains…

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

Business optimisation has been used extensively to determine optimal solutions for challenging business operations. Problem formulation is an important part of business optimisation as it influences both the validity of solutions and the…

This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods…

Large Language Models (LLMs) possess substantial reasoning capabilities and are increasingly applied to optimization tasks, particularly in synergy with evolutionary computation. However, while recent surveys have explored specific aspects…

Large language models (LLMs) excel in general tasks but struggle with domain-specific ones, requiring fine-tuning with specific data. With many open-source LLMs available, selecting the best model for fine-tuning downstream tasks is…

Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…

Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…

While Large Language Models (LLMs) demonstrate remarkable reasoning, complex optimization tasks remain challenging, requiring domain knowledge and robust implementation. However, existing benchmarks focus narrowly on Mathematical…

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm…

Real-world path planning tasks typically involve multiple constraints beyond simple route optimization, such as the number of routes, maximum route length, depot locations, and task-specific requirements. Traditional approaches rely on…

In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…

Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

The maximum hands-off control is the optimal solution to the L0 optimal control problem. It has the minimum support length among all feasible control inputs. To avoid computational difficulties arising from its combinatorial nature, the…

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in…