This paper is an introduction to Newton, a constraint programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) languages over intervals with advanced interval tcchniqucs dcvclopcd in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of ...

This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the trust cylinder is violated, a restoration step is called and the infeasibility level is reduced. The radius of the trust cylinder has a nonincreasing update scheme, so eventually ...

Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grr obner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The pr...

A stochastic framework combining classification with nonlinear regression is proposed. The performance evaluation is tested in terms of a patch-based image superresolution problem. Assuming a multi-variate Gaussian mixture model for the distribution of all image content, unsupervised probabilistic clustering via expectation maximization allows segmentation of the domain. Subsequently, for the r...

The problem of estimating the thickness and the optical constants of thin films using transmission data only is very challenging from the mathematical point of view, and has a technological and an economic importance. In many cases it represents a very ill-conditioned inverse problem with many local-nonglobal solutions. In a recent publication we proposed nonlinear programming models for solvin...

In this paper we interpret chaos synchronization schemes within the framework of Lagrange programming networks, which form a class of continuous-time optimization methods for solving constrained nonlinear optimization problems. From this study it follows that standard synchronization schemes can be regarded as a Lagrange programming network with soft constraining, where synchronization between ...

We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP) Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete data integrator, in a direct solution paradigm adapted to the spreadsheet. The technique...

In this paper we apply receding horizon constrained optimal control to the computation of insulin administration for people with type 1 diabetes. The study is based on the Hovorka model, which describes a virtual subject with type 1 diabetes. First of all, we compute the optimal insulin administration for the linearized system using quadratic programming (QP) for optimization. The optimization ...

A nonlinear programming approach for the optimal motion planning of robotic manipulators is presented. In this approach a standard optimal control problem of infinite dimensionality (in time) is converted into an optimization problem of finite dimensionality by approximating the manipulator trajectories by the sum of a polynomial and a set of appropriate eigenfunctions. The optimal control prob...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...