Related papers: Verified Optimization
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
The quality and correct functioning of software components embedded in electronic systems are of utmost concern especially for safety and mission-critical systems. Model-based testing and formal verification techniques can be employed to…
The use of alternative measures to evaluate classifier performance is gaining attention, specially for imbalanced problems. However, the use of these measures in the classifier design process is still unsolved. In this work we propose a…
Artificial Intelligence (AI) is fundamentally reshaping various industries by enhancing decision-making processes, optimizing operations, and unlocking new opportunities for innovation. This paper explores the applications of AI across four…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
Automated proof assistants are a technology pre-empting mistakes in mathematics. In our practice we have seen that reasoning about planar diagrams is difficult to both humans and computers. One example that has led to wrong statements in…
This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
Virtualization is gaining attraction in the industry as it promises a flexible way to integrate, manage, and re-use heterogeneous software components with mixed-criticality levels, on a shared hardware platform, while obtaining isolation…
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 paper introduces a novel Large Language Models (LLMs)-assisted agent that automatically converts natural-language descriptions of power system optimization scenarios into compact, solver-ready formulations and generates corresponding…
This article studies the existing methods of virtualization of different resources. The positive and negative aspects of each of the methods are analyzed, the perspectivity of the approach is noted. It is also made an attempt to classify…
Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
In many important design problems, some decisions should be made by finding the global optimum of a multiextremal objective function subject to a set of constrains. Frequently, especially in engineering applications, the functions involved…
Modelling, simulation and optimization form an integrated part of modern design practice in engineering and industry. Tremendous progress has been observed for all three components over the last few decades. However, many challenging issues…
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…
Optimizing application performance in today's hardware architecture landscape is an important, but increasingly complex task, often requiring detailed performance analyses. In particular, data movement and reuse play a crucial role in…