Transcription of Nonlinear Programming: Concepts, Algorithms and Applications
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Nonlinear Programming: Concepts, Algorithms and Applications
Nonlinear Programming: Concepts, Algorithms and ApplicationsL. T. BieglerChemical Engineering DepartmentCarnegie Mellon UniversityPittsburgh, PA 2 IntroductionUnconstrained Optimization Algorithms Newton Methods Quasi-Newton MethodsConstrained Optimization Karush Kuhn-Tucker Conditions Special Classes of Optimization Problems Reduced Gradient Methods (GRG2, CONOPT, MINOS) Successive Quadratic Programming (SQP) Interior Point MethodsProcess Optimization Black Box Optimization Modular Flowsheet Optimization Infeasible Path The Role of Exact DerivativesLarge-Scale Nonlinear Programming Data Reconciliation Real-time Process OptimizationFurther Applications Sensitivity Analysis for NLP Solutions Multiperiod Optimization ProblemsSummary and ConclusionsNonlinear Programming and Process Optimization3 IntroductionOptimization: given a system or process, find the best solution to this process within Function: indicator of "goodness" of solution, , cost, yield, profit, : variables that influence process behavior and can be adjusted for many cases, this task is done by trial and error (through case study).
• Identity Matrix - I, square matrix with ones on diagonal and zeroes elsewhere. • Determinant: "Inverse Volume" measure of a square matrix det(A) = Σi (-1)i+j Aij Aij for any j, or det(A) = Σj (-1)i+j Aij Aij for any i, where Aij is the determinant of an order n-1matrix with row i and column j removed. det(I) = 1 • Singular Matrix: det ...
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