Knitro: An Integrated Package for Nonlinear Optimization

This paper describes Knitro 5.0, a C-package for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving large-scale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, … Read more

Experimental Datasets from Chemical Thermodynamics

I have been working for quite awhile with the treatment of experimental results in chemical thermodynamics. I have tried to organize my archives and make them available for others. There are several experimental datasets in computer readable format and I hope that they can be used as useful benchmarks for data fitting and nonlinear optimization. … Read more

A generating set search method exploiting curvature and sparsity

Generating Set Search method are one of the few alternatives for optimising high fidelity functions with numerical noise. These methods are usually only efficient when the number of variables is relatively small. This paper presents a modification to an existing Generating Set Search method, which makes it aware of the sparsity structure of the Hessian. … Read more

Perturbation analysis of second order programming problems

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions. Citation Research Report 5293 (August … Read more

Recursive Trust-Region Methods for Multilevel Nonlinear Optimization (Part I): Global Convergence and Complexity

A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is recursive, leading to … Read more

Optimality Measures for Performance Profiles

We examine the importance of optimality measures when benchmarking a set of solvers, and show that scaling requirements lead to a convergence test for nonlinearly constrained optimization solvers that uses a mixture of absolute and relative error measures. We demonstrate that this convergence test is well behaved at any point where the constraints satisfy the … Read more

An algorithm model for mixed variable programming

In this paper we consider a particular class of nonlinear optimization problems involving both continuous and discrete variables. The distinguishing feature of this class of nonlinear mixed optimization problems is that the structure and the number of variables of the problem depend on the values of some discrete variables. In particular we define a general … Read more

On the Convergence of Successive Linear Programming Algorithms

We analyze the global convergence properties of a class of penalty methods for nonlinear programming. These methods include successive linear programming approaches, and more specifically the SLP-EQP approach presented in \cite{ByrdGoulNoceWalt02}. Every iteration requires the solution of two trust region subproblems involving linear and quadratic models, respectively. The interaction between the trust regions of these … Read more

New Classes of Globally Convexized Filled Functions for Global Optimization

We propose new classes of globally convexized filled functions. Unlike the globally convexized filled functions previously proposed in literature, the ones proposed in this paper are continuously differentiable and, under suitable assumptions, their unconstrained minimization allows to escape from any local minima of the original objective function. Moreover we show that the properties of the … Read more

iNEOS : An Interactive Environment for Nonlinear Optimization

In this paper we describe iNEOS, an Internet-based environment which facilitates the solution of complex nonlinear optimization problems. It enables a user to easily invoke a remote optimization code without having to supply the model to be optimized. An interactive communication between client and server is established and maintainted using CORBA. We test the system … Read more