The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
A deterministic spatial branch and bound global optimization algorithm is presented for systems with an initial value problem for a set of first-order, typically nonlinear, differential equations in the constraints. Upper bounds on the global minimum are obtained using the sequential approach for the local solution of the dynamic optimization problem. The solution of a convex relaxation of the problem...
We present an exact algorithm and three applications of nonconvex quadratically constrained quadratic programming. First, we consider the pooling problem from the oil industry, and apply the algorithm to standard problems from the literature. Second, we apply the algorithm to fractional programming problems, which arise in finance. Finally, we show how it can be used to find the largest small octagon,...
In this contribution, we will focus on problems arising in the context of biochemical process engineering. Many of these problems can be stated as the optimization of non-linear dynamic systems. Relevant classes in this domain are (i) optimal control problems (dynamic optimization), (ii) inverse problems (parameter estimation), and (iii) simultaneous design and control optimization problems. Most...
The prediction of the tridimensional structure of a molecule can be formulated as a global minimization problem. The main difficulty of this problem is the exponential growth of the number of local minima of the molecular potential energy function with respect to the size of the molecule. We propose a steady-state real-coded genetic algorithm to search for the global minimum. Several recombination...
This paper presents an alternative approach to the deterministic global optimisation of problems with ordinary differential equations in the constraints. The algorithm uses a spatial branch-and-bound approach and a novel procedure to build convex underestimation of nonconvex problems is developed. Each nonconvex functional in the original problem is underestimated by adding a separate convex quadratic...
Given a system of linear relations, we consider the problem of finding a maximum feasible subsystem, that is a solution satisfying as many relations as possible. This general problem, called MAX FLS, is equivalent to the Closed Hemisphere Problem, which was shown to be NP-complete by Johnson and Preparata. MAX FLS is also equivalent to the problem of computing the location depth of a point p relative...
This paper addresses the problem of finding tight affine lower bound functions for multivariate polynomials. Such underestimating functions are needed if global optimization problems involving polynomials are solved with a branch and bound method. These bound functions are constructed by using the expansion of the given polynomial into Bernstein polynomials. In contrast to our previous method which...
There are a variety of problems in production planning, transportation, finance, inventory, resource allocation and elsewhere where a guaranteed global optimum, rather than just a local optimum, is desired. Probabilistic approaches, based on various ideas such as using random multiple start points with the algorithms, have been useful. It would be satisfying, however, to have a guarantee of finding...
Significant advances have been made in the last two decades for the effective solution of Mixed Integer Non-Linear Programming (MINLP) problems, mainly by exploiting the special structure of the problem that results under certain convexity assumptions. A number of decomposition based algorithms have been developed based on the concepts of projection, outer approximation and relaxation. For the case...
Many well-structured problems in many areas can be defined as the optimization of a multivariate energy function E(x1,x2,…,xn). In most cases, a problem of that type is computationally hard. The only way we know before to find the global optimum is by making an algorithm that runs in exponential time which is too expensive in practice. The other traditional methods,...
We consider finite dimensional smooth optimization problems with a compact and connected feasible set. A basic problem in global optimization is how to get from one local minimum to all other ones by using local ascent or descent directions. In general, these local directions are induced by a Riemannian (i.e. variable) metric. We consider the “bang-bang” strategy of starting at a local minimum, going...
The goal of this project was to compute minimal cost solutions satisfying the demand of pre-given product portfolios and to investigate the dependence of the fix costs and investment costs on the product portfolio. The most important parameters characterizing the production facilities are the number and the size of the reactors. The production is subject to shelf-life constraints, i.e., products...
In the field of deterministic structural optimization, the designer reduces the structural cost without taking into account uncertainties concerning materials, geometry and loading. This way the resulting optimal design may represent a lower level of reliability and thus a higher risk of failure. The integration of reliability analysis into the design optimization problem represents the Reliability-Based...
One of the important points in molecular conformation problems is the evaluation of the gradient and Hessian of potential energy functions. These functions consist of a set of energy contributions, called the force field, for approximating the interactions between atoms of a molecule. Our discussion will focus on potential energy functions that have most common terms in general force fields. We can...
Hybrid systems, which exhibit both discrete state and continuous state behavior, have become the modeling framework of choice for a wide variety of applications that require detailed dynamic models with embedded discontinuities. Economic, environmental, safety and quality considerations in these applications, such as the automated design of safe operating procedures and the formal verification of...
This paper analyzes and evaluates an efficient n-dimensional global optimization algorithm. It is an extended version of the algorithm of Casado et al. [1]. This algorithm takes advantage of all available information to estimate better bounds of the function. Numerical comparison made on a class of multiextremal test functions has shown that on average the new algorithm works faster than a traditional...
Approximations of the convex envelope of nonconvex functions play a central role in deterministic global optimization algorithms and the efficiency of these algorithms is highly infuenced by the tightness of these approximations. McCormick (1976), and AlKhayyal and Falk (1983) have shown how to construct the convex envelope of individual bilinear terms over a rectangular domain. Rikun (1997) has shown...
In this work we propose a general procedure for analyzing global minima of arbitrary mathematical programs which is based in probability measures and moments theory. We give a general characterization of global minima of arbitrary programs, and as a particular case, we characterize the global minima of unconstrained one dimensional polynomial programs by using a particular semidefinite program.
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.