Alberto Lovison

University of Padova | UNIPD · Department of Mathematics

In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish to integrate the well-known (dynamic) theory of Pontryagin optimal control with the Pareto optimization (of the static type), involving the maximization/minimization of a non-trivial number of functions or functionals, Pontryagin optimal c...

Significance For most of its path through plant bodies, water moves in conduits in the wood. Plant water conduction is crucial for Earth’s biogeochemical cycles, making it important to understand how natural selection shapes conduit diameters along the entire lengths of plant stems. Can mathematical modeling and global sampling explain how wood con...

Deterministic global optimization algorithms like Piyavskii-Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence t...

The direct algorithm has been recognized as an efficient global optimization method which has few requirements of regularity and has proven to be globally convergent in general cases. direct has been an inspiration or has been used as a component for many multiobjective optimization algorithms. We propose an exact and as genuine as possible extensi...

In this paper we consider a nonlinear reaction–diffusion equation in which the nonlinear term is described by a potential energy function. For this class of pde, equilibria admit a variational formulation and they can be determined by a suitable finite dimensional reduction technique called Amann–Conley–Zendher (ACZ) reduction. By extension, the AC...

Real-world optimization problems may involve a number of computationally expensive functions with a large number of input variables. Metamodel-based optimization methods can reduce the computational costs of evaluating expensive functions, but this does not reduce the dimension of the search domain nor mitigate the curse of dimensionality effects....

In this paper a certain type of reaction–diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov–Schmidt reduction of the cited reaction–diffusion equat...

In this paper a reaction-diffusion type equation is the starting point for setting up a genuine thermodynamic reduction, i.e. involving a finite number of parameters or collective variables, of the initial system. This program is carried over by firstly operating a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when refo...

When large volumes of fluids are removed from or injected into underground formations for, e.g., hydrocarbon and water production, CO2 storage, gas storage, and geothermal energy exploitation, monitoring of surface deformations coupled to numerical modeling improves our understanding of reservoir behavior. The ability to accurately simulate surface...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new pattern for how the reactive dynamics of individuals is distributed across the set of each agent’s contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each diff...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to...

Lipschitz global methods for single-objective optimization can represent the optimal solutions with desired accuracy. In this paper, we highlight some directions on how the Lipschitz global methods can be extended as faithfully as possible to multiobjective optimization problems. In particular, we present a multiobjective version of the Pijavskiǐ-S...

We present an overview on the state of the art of the research on the asymptotic behavior of diffraction integrals, i.e., the oscillatory integrals employed in the Fresnel theory of optics. We focus on the behavior of such integrals in the presence of standard caustics, in particular the elliptic and the hyperbolic umbilics, adopting the functional...

In smooth and convex multiobjective optimization problems the set of Pareto optima is diffeomorphic to an $m-1$ dimensional simplex, where $m$ is the number of objective functions. The vertices of the simplex are the optima of the individual functions and the $(k-1)$-dimensional facets are the Pareto optimal set of $k$ functions subproblems. Such a...

We introduce a novel approximation method for multiobjective optimization problems called PAINT-SiCon. The method can construct consistent parametric representations of Pareto sets, especially for nonconvex problems, by interpolating between nondominated solutions of a given sampling both in the decision and objective space. The proposed method is...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new pattern for how the reactive dynamics of individuals is distributed across the set of each agent’s contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to each diff...

We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In long-term empirical data on email, we find that the set of response times considered separately for the messages to...

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through eac...

Extending the notion of global search to multiobjective optimization is far than straightforward, mainly for the reason that one almost always has to deal with infinite Pareto optima and correspondingly infinite optimal values. Adopting Stephen Smale’s global analysis framework, we highlight the geometrical features of the set of Pareto optima and...

Remote sensing techniques have been widely used in recent decades to monitor earth surface displacements related to seismic faults, volcanoes, landslides, aquifers, hydrocarbon fields. In particular, advanced InSAR techniques, such as SqueeSAR™, have already provided unique results thanks to both the extension of the area which can be monitored by...

Land subsidence and uplift due to the production/injection of fluids from/into the subsurface have been widely observed worldwide over the last decades and occur for a variety of purposes such as groundwater pumping, aquifer system recharge, gas/oil field development, enhanced oil recovery, geologic CO2 sequestration, underground gas storage and wa...

We present the exact nite reduction of a class of nonlinearly perturbed wave equations -typically, a non-linear elastic string- based on the Amann-Conley-Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral nite description derived from A-C-Z and a discrete mechanical model, a well denite nite...

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale [Global analysis and economics. I. Pareto optimum and a generalization of Morse theory, in Dynamical Systems, Academic Press, New York, 1973, pp. 531–544]. The method highlights and exploits the underlying manifold structure of the P...

Lipschitz Sampling, unlike standard space filling strategies (Minimax and Maximin distance, Integrated Mean Squared Error, Eadze-Eglais, etc.) for producing good metamodels, incorporates information from output evaluation in order to estimate in some sense the local complexity of the function at hand. The complexity indicator considered is a suitab...

We present an application of the Amann-Zehnder exact finite reduction to a class of nonlinear perturbations of elliptic elasto-static problems. We propose the existence of minmax solutions by applying Ljusternik-Schnirelmann theory to a finite dimensional variational formulation of the problem, based on a suitable spectral cut-off. As a by-product,...

Selecting the best input values for the purpose of fitting a metamodel to the response of a computer code presents several issues. Classical designs for physical experiments (DoE) have been developed to deal with noisy responses, while general space filling designs, though being usually effective for complete classes of problems, are not easily tra...

We analyze the class of networks characterized by modular structure where a sequence of l Erdös-Renyi random networks of size Nl with random average degrees is joined by links whose structure must remain immaterial. We find that traceroutes spanning the entire macronetwork exhibit scaling degree distributions P(k) approximately k-gamma, where gamma...

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hie...

The Amann–Conley–Zehnder (ACZ) reduction is a global Lyapunov–Schmidt reduction for PDEs based on spectral decomposition. ACZ has been applied in conjunction to diverse topological methods, to derive existence and multiplicity results for Hamiltonian systems, for elliptic boundary value problems, and for nonlinear wave equations. Recently, the ACZ...

In this paper we give precise asymptotic expansions and estimates of the remainder R(λ) for oscillatory integrals with non Morse phase functions, having degeneracies of any order k ≥ 2. We provide an algorithm for writing down explicitly the coefficients of the asymptotic expansion analysing precisely the combinatorial behaviour of the coefficients...

Neural networks (NN) are a very efficient and powerful function approximation tool. Inspired by the brain structure and functions, NN are usually trained with backpropagation learning algorithm. A detailed benchmark on standard functions is provided, supporting in particular the automatic choice of the number of neurons in the hidden layer.

In this paper we propose the numerical solution of a steady-state reaction-diffusion problem by means of application of a non-local Lyapunov–Schmidt type reduction originally devised for field theory. A numerical algorithm is developed on the basis of the discretization of the differential operator by means of simple finite differences. The eigende...

The Stationary Phase Principle (SPP) states that in the computation of oscillatory integrals, the contributions of non-stationary points of the phase are smaller than any power n of 1/k, for k. Unfortunately, SPP says nothing about the possible growth in the constants in the estimates with respect to the powers n. A quantitative estimate of oscilla...

In questa tesi si affronta uno studio sistematico di rivisitazione dell’ottica ondulatoria basato sull’equazione di Helmholtz con particolari enfasi su taluni aspetti legati alla ricerca di soluzioni globalmente definite e alle ostruzioni all'esistenza di esse: le caustiche. Le strutture simplettiche si sono rilevate il contesto adeguato nel quale...

. We consider the problem of approximating the fastest trajectory for a racing motorbike in a given circuit. This problem is important for the competitions because the performances of motorbikes are strongly affected by the chosen trajectories. We adopt a direct approach, i.e., we parametrize a family of trajectories and proceed as for standard non...

Radial Basis Functions (RBF) are a powerful tool for multivariate scattered data interpolation. Scattered data means that the training points do not need to be sampled on a regular grid: in fact RBF is a proper meshless method. Since RBF are interpolant response surfaces they pass exactly through training points. There exists a vast body of literat...

Robust design optimization is a modeling methodology, combined with a suite of computational tools, which is aimed to solve problems where some kind of uncertainty occurs in the data or in the model. This paper explores robust optimization complexity in the multiobjective case, describing a new approach by means of Polynomial Chaos expansions (PCE)...