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On the formulation and theory of Newton interior point methods for nonlinear programming
 JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
, 1996
"... In this work, we first study in detail the formulation of the primaldual interiorpoint method for linear programming. We show that, contrary to popular belief, it cannot be viewed.as adamped Newton method applied to the KarushKuhnTucker conditions for the logarithmic barrier function problem. N ..."
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In this work, we first study in detail the formulation of the primaldual interiorpoint method for linear programming. We show that, contrary to popular belief, it cannot be viewed.as adamped Newton method applied to the KarushKuhnTucker conditions for the logarithmic barrier function problem. Next, we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Qquadratically convergent under only the standard Newton method assumptions. We also establish a global convergence theory for this algorithm and include promising numerical experimentation.
An Inexact TrustRegion FeasiblePoint Algorithm for Nonlinear Systems of Equalities and Inequalities
 DEPARTMENT OF COMPUTATIONAL AND APPLIED MATHEMATICS, RICE UNIVERSITY
, 1995
"... In this work we define a trustregion feasiblepoint algorithm for approximating solutions of the nonlinear system of equalities and inequalities F(x, y) = 0, y ≥ 0, where F: R^n × R^m → R^p is continuously differentiable. This formulation is quite general; the KarushKuhn ..."
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In this work we define a trustregion feasiblepoint algorithm for approximating solutions of the nonlinear system of equalities and inequalities F(x, y) = 0, y &ge; 0, where F: R^n &times; R^m &rarr; R^p is continuously differentiable. This formulation is quite general; the KarushKuhnTucker conditions of a general nonlinear programming problem are an obvious example, and a set of equalities and inequalities can be transformed, using slack variables, into such form. We will be concerned with the possibility that n, m, and p may be large and that the Jacobian matrix may be sparse and rank deficient. Exploiting the convex structure of the local model trustregion subproblem, we propose a globally convergent inexact trustregion feasiblepoint algorithm to minimize an arbitrary norm of the residual, say F(x, y)a, subject to the nonnegativity constraints. This algorithm uses a trustregion globalization strategy to determine a descent direction as an inexact solution of the local model trustregion subproblem and then, it uses linesearch techniques to obtain an acceptable steplength. We demonstrate that, under rather weak hypotheses, any accumulation point of the iteration sequence is a constrained stationary point for f = Fa, and that the sequence of constrained residuals converges to zero.
Representation,analysis And Solution Of Conditional Models In An EquationBased Environment
, 1998
"... Process modeling is an important task in many process engineering activities. At the lowest level, process models are represented by a large set of variables and a large system of linear and nonlinear equations that relate them. The equationbased modeling approach has been demonstrated as effective ..."
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Process modeling is an important task in many process engineering activities. At the lowest level, process models are represented by a large set of variables and a large system of linear and nonlinear equations that relate them. The equationbased modeling approach has been demonstrated as effective in solving simulation, optimization, parameter estimation and data reconciliation problems. Even though many currently available equationbased modeling systems have been reported in the literature, most of them give little or no attention to conditional models. Conditional models exist when the equations defining a system depend on where the model solution lies. Examples of conditional models in chemical engineering are systems involving physicochemical discontinuities such as flow and phase transitions. This work investigates the setting up and solving of conditional models within an equationbased modeling environment. We first describe modeling tools for the efficient representation of ...