arXiv subjects

Pierluigi Mansueto

Publications and source records attributed to Pierluigi Mansueto.

13 recordsLinked to original sources

arXiv2026

Nonconvex optimization methods for ground states in disordered continuous-spin models

This work explores the global optimization problem of finding lowest-energy configurations in disordered continuous-spin models from statistical physics, with a particular focus on the random field XY model. Due to an extremely non-convex nature of the associated energy landscape, this problem remains highly challenging. From an optimization perspective, we reformulate the traditional angular Hamiltonian as a constrained problem on the Cartesian product of spheres, allowing the application of Riemannian optimization techniques, which show better computational performance. We design a family of Basin Hopping algorithms whose perturbation mechanisms are specifically designed to exploit the structure of the underlying physical model, and further extend them within a Population Basin Hopping framework. The proposed methods are evaluated against optimization algorithms widely used in computational physics. The proposed variants turn out to be the most effective method in the comparison, consistently attaining lower-energy configurations within the same computational budget. This work establishes a robust link between continuous-spin systems and continuous global optimization, providing a high-performance benchmark for exploring complex energy landscapes.

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arXiv2026

A heavy-ball type curve search method for smooth convexly constrained optimization

This paper addresses smooth convexly constrained optimization problems where the Euclidean projection onto the feasible set is computationally tractable. Although momentum techniques like Polyak's heavy-ball are known for accelerating optimization algorithms, their use in constrained settings remains limited due to challenges in preserving feasibility and ensuring convergence. We thus propose a heavy-ball-type method that extends to the constrained case a recently introduced curve-search globalization framework. The method attempts a momentum update and performs a curvilinear search to enforce an Armijo-type descent condition: when the momentum step is infeasible or unacceptable, the algorithm smoothly reverts to a feasible descent direction. We prove that the algorithm is well-defined and globally convergent to stationary points; the derivation of these results is nontrivial due to the use of a heavy-ball type direction in a constrained setting, where it may generate infeasible iterates. We discuss the incorporation of further mechanisms into the algorithm, including non-monotone curve search, spectral steplength selection and an adaptive momentum strategy. Numerical experiments on benchmark problems show the method is robust and competitive with the state-of-the-art.

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arXiv2025

Projection-based curve pattern search for black-box optimization over smooth convex sets

In this paper, we deal with the problem of optimizing a black-box smooth function over a full-dimensional smooth convex set. We study sets of feasible curves that allow to properly characterize stationarity of a solution and possibly carry out sound backtracking curvilinear searches. We then propose a general pattern search algorithmic framework that exploits curves of this type to carry out poll steps and for which we prove properties of asymptotic convergence to stationary points. We particularly point out that the proposed framework covers the case where search curves are arcs induced by the Euclidean projection of coordinate directions. The method is finally proved to arguably be superior, on smooth problems, than other recent projection-based algorithms and is competitive with state-of-the-art methods from the literature on constrained black-box optimization.

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arXiv2025

A Nonmonotone Front Descent Method for Bound-Constrained Multi-Objective Optimization

We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the first descent algorithm employing nonmonotone strategies to generate point sets approximating the Pareto front. We establish convergence properties for the resulting sequences of sets, analogous to the original framework, and present numerical results confirming the approach's consistency in the bound-constrained setting.

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arXiv2025

Effective Front-Descent Algorithms with Convergence Guarantees

In this manuscript, we address continuous unconstrained multi-objective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we analyze the class of Front Descent methods, which generalizes the Front Steepest Descent algorithm allowing the employment of suitable, effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We provide a deep characterization of the behavior and the mechanisms of the algorithmic framework, and we prove that, under reasonable assumptions, standard convergence results and some complexity bounds hold for the generalized approach. Moreover, we prove that popular search directions can indeed be soundly used within the framework. Then, we provide a completely novel type of convergence results, concerning the sequence of sets produced by the procedure. In particular, iterate sets are shown to asymptotically approach stationarity for all of their points; the convergence result is accompanied by a worst-case iteration complexity bound; additionally, in finite precision settings, the sets are shown to only be enriched through exploration steps in later iterations, and suitable stopping conditions can be devised. Finally, the results from a large experimental benchmark show that the proposed class of approaches far outperforms state-of-the-art methodologies.

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arXiv2025

Efficient globalization of heavy-ball type methods for unconstrained optimization based on curve searches

In this work, we deal with unconstrained nonlinear optimization problems. Specifically, we are interested in methods carrying out updates possibly along directions not of descent, like Polyak's heavy-ball algorithm. Instead of enforcing convergence properties through line searches and modifications of search direction when suitable safeguards are not satisfied, we propose a strategy based on searches along curve paths: a curve search starting from the first tentative update allows to smoothly revert towards a gradient-related direction if a sufficient decrease condition is not met. The resulting algorithm provably possesses global convergence guarantees, even with a nonmonotone decrease condition. While the presented framework is rather general, particularly of interest is the case of parabolic searches; in this case, under reasonable assumptions, the resulting algorithm can be shown to possess optimal worst case complexity bounds for reaching approximate stationarity in nonconvex settings. Practically, we show that the proposed globalization strategy allows to consistently accept (optimal) pure heavy-ball steps in the strongly convex case, while standard globalization approaches would at times negate them before even evaluating the objective function. Preliminary computational experiments also suggest that the proposed framework might be more convenient than classical safeguard based approaches.

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arXiv2025

Combining Gradient Information and Primitive Directions for High-Performance Mixed-Integer Optimization

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit derivative information when possible in these scenarios: concretely, we propose an algorithmic framework that carries out local optimization steps, alternating searches along gradient-based and primitive directions. The algorithm is shown to match the convergence properties of a derivative-free counterpart. Most importantly, the results of thorough computational experiments show that the proposed method clearly outperforms not only the derivative-free approach but also the main alternatives available from the literature to be used in the considered setting, both in terms of efficiency and effectiveness.

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arXiv2024

Optimization-Driven Design of Monolithic Soft-Rigid Grippers

Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated designs, requiring multiple prototypes before achieving a functional system. In this study, we propose a novel methodology to address these limitations by combining advanced rapid prototyping techniques and an efficient optimization strategy. Firstly, we employ rapid prototyping methods typically used for rigid structures, leveraging their precision to fabricate compliant components with reduced manufacturing errors. Secondly, our optimization framework minimizes the need for extensive prototyping, significantly reducing the iterative design process. The methodology enables the identification of stiffness parameters that are more practical and achievable within current manufacturing capabilities. The proposed approach demonstrates a substantial improvement in the efficiency of prototype development while maintaining the desired performance characteristics. This work represents a step forward in bridging the sim-to-real gap in soft robotics, paving the way towards a faster and more reliable deployment of soft robotic systems.

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arXiv2024

Memetic Differential Evolution Methods for Semi-Supervised Clustering

In this paper, we propose an extension for semi-supervised Minimum Sum-of-Squares Clustering (MSSC) problems of MDEClust, a memetic framework based on the Differential Evolution paradigm for unsupervised clustering. In semi-supervised MSSC, background knowledge is available in the form of (instance-level) "must-link" and "cannot-link" constraints, each of which indicating if two dataset points should be associated to the same or to a different cluster, respectively. The presence of such constraints makes the problem at least as hard as its unsupervised version and, as a consequence, some framework operations need to be carefully designed to handle this additional complexity: for instance, it is no more true that each point is associated to its nearest cluster center. As far as we know, our new framework, called S-MDEClust, represents the first memetic methodology designed to generate a (hopefully) optimal feasible solution for semi-supervised MSSC problems. Results of thorough computational experiments on a set of well-known as well as synthetic datasets show the effectiveness and efficiency of our proposal.

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arXiv2024

A Bi-Objective Optimization Based Acquisition Strategy for Batch Bayesian Global Optimization

In this paper, we deal with batch Bayesian Optimization (Bayes-Opt) problems over a box and we propose a novel bi-objective optimization (BOO) acquisition strategy to sample points where to evaluate the objective function. The BOO problem involves the Gaussian Process posterior mean and variance functions, which, in most of the acquisition strategies from the literature, are generally used in combination, frequently through scalarization. However, such scalarization could compromise the Bayes-Opt process performance, as getting the desired trade-off between exploration and exploitation is not trivial in most cases. We instead aim to reconstruct the Pareto front of the BOO problem based on optimizing both the posterior mean as well as the variance, thus generating multiple trade-offs without any a priori knowledge. The reconstruction is performed through the Non-dominated Sorting Memetic Algorithm (NSMA), recently proposed in the literature and proved to be effective in solving hard MOO problems. Finally, we present two clustering approaches, each of them operating on a different space, to select potentially optimal points from the Pareto front. We compare our methodology with well-known acquisition strategies from the literature, showing its effectiveness on a wide set of experiments.

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arXiv2023

Cardinality-Constrained Multi-Objective Optimization: Novel Optimality Conditions and Algorithms

In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective optimization, we define the concept of L-stationarity and we analyze its relationships with other existing conditions and Pareto optimality concepts. We then propose two novel algorithmic approaches: the first one is an Iterative Hard Thresholding method aiming to find a single L-stationary solution, while the second one is a two-stage algorithm designed to construct an approximation of the whole Pareto front. Both methods are characterized by theoretical properties of convergence to points satisfying necessary conditions for Pareto optimality. Moreover, we report numerical results establishing the practical effectiveness of the proposed methodologies.

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arXiv2023

Improved Front Steepest Descent for Multi-objective Optimization

In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus introduce some modifications within the algorithm aimed to overcome this significant limitation. We prove that the asymptotic convergence properties of the algorithm are preserved and numerically show that the proposed method significantly outperforms the original one.

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arXiv2022

A Memetic Procedure for Global Multi-Objective Optimization

In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm (NSMA), besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions.

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