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On the Implementation of an InteriorPoint Filter LineSearch Algorithm for LargeScale Nonlinear Programming
, 2004
"... We present a primaldual interiorpoint algorithm with a lter linesearch method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phas ..."
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Cited by 283 (6 self)
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We present a primaldual interiorpoint algorithm with a lter linesearch method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, secondorder corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several linesearch options, and a comparison is provided with two stateoftheart interiorpoint codes for nonlinear programming.
An interior point algorithm for largescale nonlinear . . .
, 2002
"... Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes ..."
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Cited by 62 (3 self)
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Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes reach their practical limits. The objective of this dissertation is the design, analysis, implementation, and evaluation of a new NLP algorithm that is able to overcome the current bottlenecks, particularly in the area of process engineering. The proposed algorithm follows an interior point approach, thereby avoiding the combinatorial complexity of identifying the active constraints. Emphasis is laid on exibility in the computation of search directions, which allows the tailoring of the method to individual applications and is mandatory for the solution of very large problems. In a fullspace version the method can be used as general purpose NLP solver, for example in modeling environments such as Ampl. The reduced space version, based on coordinate decomposition, makes it possible to tailor linear algebra
Failure of global convergence for a class of interior point methods for nonlinear programming
 Mathematical Programming
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Advances in Simultaneous Strategies for Dynamic Process Optimization
 Optimization, Chemical Engineering Science
, 2001
"... Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the develop ..."
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Cited by 34 (7 self)
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Introduction Over the past decade, applications in dynamic simulation have increased signicantly in the process industries. These are driven by strong competitive markets faced by operating companies along with tighter specications on process performance and regulatory limits. Moreover, the developmentofpowerful commercial modeling tools for dynamic simulation, such as ASPEN Custom # ####### ########################## #### ############### ################### 1 Modeler and gProms, has led to their introduction in industry alongside their widely used steady state counterparts. Dynamic optimization is the natural extension of these dynamic simulation tools because it automates many of the decisions required for engineering studies. Applications of dynamic simulation can be classied into oline and online tasks. Oline tasks include: # Design to avoid undesirable transients for chemical process
Feasible Interior Methods Using Slacks for Nonlinear Optimization
 Computational Optimization and Applications
, 2002
"... A slackbased feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust regio ..."
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Cited by 20 (2 self)
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A slackbased feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is effective for problems containing both equality and inequality constraints. The relationship between slackbased methods and traditional feasible methods is discussed. Numerical results showing the relative performance of feasible versus infeasible interior point methods are presented.
Global and local convergence of line search filter methods for nonlinear programming
, 1521
"... Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and ..."
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Cited by 18 (4 self)
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Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior point and active set SQP algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. Furthermore, it is shown that the proposed methods do not suffer from the Maratos effect if the search directions are improved by second order corrections, so that fast local convergence to strict local solutions is achieved. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.
A Convergent Infeasible InteriorPoint TrustRegion Method For Constrained Minimization
 SIAM Journal on Optimization
, 1999
"... We study an infeasible interiorpoint trustregion method for constrained minimization. This method uses a logarithmicbarrier function for the slack variables and updates the slack variables using secondorder correction. We show that if a certain set containing the iterates is bounded and the orig ..."
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Cited by 16 (0 self)
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We study an infeasible interiorpoint trustregion method for constrained minimization. This method uses a logarithmicbarrier function for the slack variables and updates the slack variables using secondorder correction. We show that if a certain set containing the iterates is bounded and the origin is not in the convex hull of the nearly active constraint gradients everywhere on this set, then any cluster point of the iterates is a 1storder stationary point. If the cluster point satisfies an additional assumption (which holds when the constraints are linear or when the cluster point satisfies strict complementarity and a local error bound holds), then it is a 2ndorder stationary point. Key words. Nonlinear program, logarithmicbarrier function, interiorpoint method, trustregion strategy, 1st and 2ndorder stationary points, semidefinite programming. 1 Introduction We consider the nonlinear program with inequality constraints: minimize f(x) subject to g(x) = [g 1 (x) g m (...
A Reduced Space Interior Point Strategy for Optimization of Differential Algebraic Systems
 Computers & Chemical Engineering
, 1999
"... A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear pr ..."
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Cited by 13 (5 self)
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A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of differential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear programming. These applications often consist of large, complex nonlinear models that result from discretizations of DAEs. Variables in the NLP model include state and control variables, with far fewer control variables than states. Moreover, all of these discretized variables have associated upper and lower bounds which can be potentially active. To deal with this large, highly constrained problem, an interior point NLP strategy is developed. Here a log barrier function is used to deal with the large number of bound constraints in order to transform the problem to an equality constrained NLP. A modified Newton method is then applied directly to this problem. In addition, this method uses an efficient decomposition of the discretized DAEs and the solution of the Newton step is performed in the reduced space of the independent variables. The resulting approach exploits many of the features of the DAE system and is performed element by element in a forward manner. Several large dynamic process optimization problems are considered to demonstrate the effectiveness of this approach; these include complex separation and reaction processes (including reactive distillation) with several hundred DAEs. NLP formulations with over 55,000 variables are considered. These problems are solved in 5 to 12 CPU minutes on small workstations. Key words: interior point; dynamic optimization; nonlinear programming 1 1
Tits, A Simple primaldual feasible interiorpoint method for nonlinear programming with monotone descent
 Computational Optimization and Applications
, 2003
"... We propose and analyze a primaldual interior point method of the “feasible ” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of bett ..."
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Cited by 12 (2 self)
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We propose and analyze a primaldual interior point method of the “feasible ” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from nonKKT stationary points. Assets of the proposed scheme include relative simplicity of the algorithm and of the convergence analysis, strong global and local convergence properties, and good performance in preliminary tests. In addition, the initial point is allowed to lie on the boundary of the feasible set.