Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive research question. To address these issues, we explore how data-driven approaches can accelerate the solution process. Aiming at high-accuracy solutions, we focus on a stabilized interior-point solver and carefully handle its two-loop flow and control parameters. We will show that reinforcement learning can make a significant contribution to facilitating the solver tuning and to speeding up the optimization process. Numerical experiments demonstrate that, after a lightweight training, the learned policy generalizes well to different problem classes with varying dimensions and to various solver configurations.

Recent advances in large language models (LLMs) have shown impressive performance in mathematical reasoning and code generation. However, LLMs still struggle in the simulation domain, particularly in generating Simulink models, which are essential tools in engineering and scientific research. Our preliminary experiments indicate that LLM agents often fail to produce reliable and complete Simulink simulation code from text-only inputs, likely due to the lack of Simulink-specific data in their pretraining. To address this challenge, we propose SimuGen, a multimodal agent-based framework that automatically generates accurate Simulink simulation code by leveraging both the visual Simulink diagram and domain knowledge. SimuGen coordinates several specialized agents, including an investigator, unit test reviewer, code generator, executor, debug locator, and report writer, supported by a domain-specific knowledge base. This collaborative and modular design enables interpretable, robust, and reproducible Simulink simulation generation. Our source code is publicly available at https://github.com/renxinxing123/SimuGen_beta.

We discuss the issue of finding a good mathematical programming solver configuration for a particular instance of a given problem, and we propose a two-phase approach to solve it. In the first phase we learn the relationships between the instance, the configuration and the performance of the configured solver on the given instance. A specific difficulty of learning a good solver configuration is that parameter settings may not all be independent; this requires enforcing (hard) constraints, something that many widely used supervised learning methods cannot natively achieve. We tackle this issue in the second phase of our approach, where we use the learnt information to construct and solve an optimization problem having an explicit representation of the dependency/consistency constraints on the configuration parameter settings. We discuss computational results for two different instantiations of this approach on a unit commitment problem arising in the short-term planning of hydro valleys. We use logistic regression as the supervised learning methodology and consider CPLEX as the solver of interest.

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances have the same number of decision variables and constraints. On one hand, using the default solver configuration leads to suboptimal solutions. On the other hand, searching and evaluating a large number of configurations for every problem instance is time-consuming and, in some cases, infeasible. In this study, we aim to predict configuration parameters for unseen problem instances that yield lower-cost solutions without the time overhead of searching-and-evaluating configurations at the solving time. Toward that goal, we first investigate the cost correlation of MILP problem instances that come from the same distribution when solved using different configurations. We show that instances that have similar costs using one solver configuration also have similar costs using another solver configuration in the same runtime environment. After that, we present a methodology based on Deep Metric Learning to learn MILP similarities that correlate with their final solutions' costs. At inference time, given a new problem instance, it is first projected into the learned metric space using the trained model, and configuration parameters are instantly predicted using previously-explored configurations from the nearest neighbor instance in the learned embedding space. Empirical results on real-world problem benchmarks show that our method predicts configuration parameters that improve solutions' costs by up to 38% compared to existing approaches.

The game of Sokoban is an interesting platform for algorithm research. It is hard for humans and computers alike. Even small levels can take a lot of computation for all known algorithms. In this paper we will describe how a search based Sokoban solver can be structured and which algorithms can be used to realize each critical part. We implement a variety of those, construct a number of different solvers and combine them into an algorithm portfolio. The solver we construct this way can outperform existing solvers when run in parallel, that is, our solver with 16 processors outperforms the previous sequential solvers.