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Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and…
Metaheuristic search algorithms look for solutions that either maximise or minimise a set of objectives, such as cost or performance. However most real-world optimisation problems consist of nonlinear problems with complex constraints and…
Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that…
Over the last three decades more then sixty meta-heuristic algorithms have been proposed by the various authors. Such algorithms are inspired from physical phenomena, animal behavior or evolutionary concepts. These algorithms have been…
Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities…
We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce \textbf{HeurAgenix}, a…
Production planning must account for uncertainty in a production system, arising from fluctuating demand forecasts. Therefore, this article focuses on the integration of updated customer demand into the rolling horizon planning cycle. We…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Research in unsupervised text generation has been gaining attention over the years. One recent approach is local search towards a heuristically defined objective, which specifies language fluency, semantic meanings, and other task-specific…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
We present a non-convex optimization algorithm metaheuristic, based on the training of a deep generative network, which enables effective searching within continuous, ultra-high dimensional landscapes. During network training, populations…