Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

Non-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

MURAME parameter setting for creditworthiness evaluation: data-driven optimization

In this paper, we amend a multi-criteria methodology known as MURAME, to evaluate the creditworthiness of a large sample of Italian Small and Medium-sized Enterprises, using as input their balance sheet data. This methodology produces results in terms of scoring and of classification into homogeneous rating classes. A distinctive goal of this paper is to consider a preference disaggregation method to endogenously determine some parameters of MURAME, by solving a nonsmooth constrained optimization problem. Because of the complexity of the involved mathematical programming problem, for its solution we use an evolutionary metaheuristic, coupled with a specific efficient initialization. This is combined with an unconstrained reformulation of the problem, which provides a reasonable compromise between the quality of the solution and the computational burden. An extensive numerical experience is reported, comparing an exogenous choice of MURAME parameters with our approach.

A single machine multi-job integer batch scheduling problem with multi due date to minimize total actual flow time

This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.

Optimal models for estimating future infected cases of COVID-19 in Oman

The recent coronavirus disease 2019 (COVID-19) outbreak is of high importance in research topics due to its fast spreading and high rate of infections across the world. In this paper, we test certain optimal models of forecasting daily new cases of COVID-19 in Oman. It is based on solving a certain nonlinear least-squares optimization problem that determines some unknown parameters in fitting some mathematical models. We also consider extension to these models to predict the future number of infection cases in Oman. The modification technique introduces a simple ratio rate of changes in the daily infected cases. This average ratio is computed by employing the rule of Al-Baali [Numerical experience with a class of self-scaling quasi-Newton algorithms, JOTA, 96 (1998), pp. 533–553], in a sense to be defined, for measuring the infection changes.

Issues on the use of a modified Bunch and Kaufman decomposition for large scale Newton’s equation

In this work, we deal with Truncated Newton methods for solving large scale (possibly nonconvex) unconstrained optimization problems. In particular, we consider the use of a modified Bunch and Kaufman factorization for solving the Newton equation, at each (outer) iteration of the method. The Bunch and Kaufman factorization of a tridiagonal matrix is an effective and stable matrix decomposition, which is well exploited in the widely adopted SYMMBK (Bunch and Kaufman in Math Comput 31:163–179, 1977; Chandra in Conjugate gradient methods for partial differential equations, vol 129, 1978; Conn et al. in Trust-region methods. MPS-SIAM series on optimization, Society for Industrial Mathematics, Philadelphia, 2000; HSL, A collection of Fortran codes for large scale scientific computation, http://www.hsl.rl.ac.uk/; Marcia in Appl Numer Math 58:449–458, 2008) routine. It can be used to provide conjugate directions, both in the case of $$1\times 1$$ 1 × 1 and $$2\times 2$$ 2 × 2 pivoting steps. The main drawback is that the resulting solution of Newton’s equation might not be gradient–related, in the case the objective function is nonconvex. Here we first focus on some theoretical properties, in order to ensure that at each iteration of the Truncated Newton method, the search direction obtained by using an adapted Bunch and Kaufman factorization is gradient–related. This allows to perform a standard Armijo-type linesearch procedure, using a bounded descent direction. Furthermore, the results of an extended numerical experience using large scale CUTEst problems is reported, showing the reliability and the efficiency of the proposed approach, both on convex and nonconvex problems.

Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations

In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Fréchet derivative. This fact it is motivated by showing different problems where the nonlinear operators that define the equation do not verify Lipschitz and Hölder condition; however, these operators verify the omega condition established. Then, the semilocal convergence balls are obtained and the R-order of convergence and error bounds can be obtained by following thee main theorem. Finally, we perform a numerical experience by solving a nonlinear Hammerstein integral equations in order to show the applicability of the theoretical results by obtaining the existence and uniqueness balls.

Numerical Investigation of Corium Coolability in Core Catcher: Sensitivity to Modeling Parameters

To avoid settling of molten materials directly on the vessel wall in severe accident sequences, the implementation of a ‘core catcher’ device in the lower plenum of sodium fast reactor designs is considered. The device is to collect, retain and cool the debris, created when the corium falls down and accumulates in the core catcher, while interacting with surrounding coolant. This Fuel-Coolant Interaction (FCI) leads to a potentially energetic heat and mass transfer process which may threaten the vessel integrity. For simulations of severe accidents, including FCI, the SIMMER code family is employed at KIT. SIMMER-III and SIMMER-IV are advanced tools for the core disruptive accidents (CDA) analysis of liquid-metal fast reactors (LMFRs) and other GEN-IV systems. They are 2D/3D multi-velocity-field, multiphase, multicomponent, Eulerian, fluid dynamics codes coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model. However, the experience of SIMMER application to simulation of corium relocation and related FCI is limited. It should be mentioned that the SIMMER code was not firstly developed for the FCI simulation. However, the related models show its basic capability in such complicate multiphase phenomena. The objective of the study was to preliminarily apply this code in a large-scale simulation. An in-vessel model based on European Sodium Fast Reactor (ESFR) was established and calculated by the SIMMER code. In addition, a sensitivity analysis on some modeling parameters is also conducted to examine their impacts. The characteristics of the debris in the core catcher region, such as debris mass and composition are compared. Besides that, the pressure history in this region, the mass of generated sodium vapor and average temperature of liquid sodium, which can be considered as FCI quantitative parameters, are also discussed. It is expected that the present study can provide some numerical experience of the SIMMER code in plant-scale corium relocation and related FCI simulation.

Comparative cognition of number and space: the case of geometry and of the mental number line

Evidence is discussed about the use of geometric information for spatial orientation and the association between space and numbers in non-human animals. A variety of vertebrate species can reorient using simple Euclidian geometry of the environmental surface layout, i.e. in accord with metric and sense (right/left) relationships among extended surfaces. There seems to be a primacy of geometric over non-geometric information in spatial reorientation and, possibly, innate encoding of the sense of direction. The hippocampal formation plays a key role in geometry-based reorientation in mammals, birds, amphibians and fish. Although some invertebrate species show similar behaviours, it is unclear whether the underlying mechanisms are the same as in vertebrates. As to the links between space and number representations, a disposition to associate numerical magnitudes onto a left-to-right-oriented mental number line appears to exist independently of socio-cultural factors, and can be observed in animals with very little numerical experience, such as newborn chicks and human infants. Such evidence supports a nativistic foundation of number–space association. Some speculation about the possible underlying mechanisms is provided together with consideration on the difficulties inherent to any comparison among species of different taxonomic groups. This article is part of a discussion meeting issue ‘The origins of numerical abilities'.