Verified global optimization for estimating the parameters of nonlinear models

Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows one to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available

Certificates of infeasibility via nonsmooth optimization

An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0802

Constraint aggregation for rigorous global optimization

Abstract In rigorous constrained global optimization, upper bounds on the objective function help to reduce the search space. Their construction requires finding a narrow box around an approximately feasible solution, verified to contain a feasible point. Approximations are easily found by local optimization, but the verification often fails. In this paper we show that even if the verification of an approximate feasible point fails, the information extracted from the local optimization can still be used in many cases to reduce the search space. This is done by a rigorous filtering technique called constraint aggregation. It forms an aggregated redundant constraint, based on approximate Lagrange multipliers or on a vector valued measure of constraint violation. Using the optimality conditions, two sided linear relaxations, the GaussJordan algorithm and a directed modified Cholesky factorization, the information in the redundant constraint is turned into powerful bounds on the feasible set. Constraint aggregation is especially useful since it also works in a tiny neighborhood of the global optimizer, thereby reducing the cluster effect. A simple introductory example demonstrates how our new method works. Extensive tests show the performance on a large benchmark

PS Poster Session - All

This document includes all poster sessions at the IBPC 2018

Sustainable Production in Food and Agriculture Engineering

This book is a collection of original research and review papers that report on the state of the art and recent advancements in food and agriculture engineering, such as sustainable production and food technology. Encompassed within are applications in food and agriculture engineering, biosystem engineering, plant and animal production engineering, food and agricultural processing engineering, storing industry, economics and production management and agricultural farms management, agricultural machines and devices, and IT for agricultural engineering and ergonomics in agriculture