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59
On the Implementation of an InteriorPoint Filter LineSearch Algorithm for LargeScale Nonlinear Programming
, 2004
"... We present a primaldual interiorpoint algorithm with a filter 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 ph ..."
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Cited by 283 (6 self)
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We present a primaldual interiorpoint algorithm with a filter 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.
KNITRO: An integrated package for nonlinear optimization
 Large Scale Nonlinear Optimization, 35–59, 2006
, 2006
"... This paper describes Knitro 5.0, a Cpackage 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 largescale, smooth nonlinear programming problems ..."
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Cited by 104 (3 self)
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This paper describes Knitro 5.0, a Cpackage 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 largescale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an activeset method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings. 1
Efficient numerical methods for nonlinear mpc and moving horizon estimation
, 2008
"... exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussi ..."
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Cited by 39 (0 self)
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exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several algorithmic ”building blocks ” that can be combined to a multitude of algorithms. We start by discussing the sequential and simultaneous approaches, the first leading to smaller, the second to more structured optimization problems. The two big families of Newton type optimization methods, Sequential Quadratic Programming (SQP) and Interior Point (IP) methods, are presented, and we discuss how to exploit the optimal control structure in the solution of the linearquadratic subproblems, where the two major alternatives are “condensing ” and band structure exploiting approaches. The second part of the paper discusses how the algorithms can be adapted to the realtime challenge of NMPC and MHE. We recall an important sensitivity result from parametric optimization, and show that a tangential solution predictor for online data can easily be generated in Newton type algorithms. We point out one important difference between SQP and IP methods: while both methods are able to generate the tangential predictor for fixed active sets, the SQP predictor even works across active set changes. We then classify many proposed realtime optimization approaches from the literature into the developed categories.
Retrospective on Optimization
 25 TH YEAR ISSUE ON COMPUTERS AND CHEMICAL ENGINEERING
"... In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of op ..."
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Cited by 36 (1 self)
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In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of optimization problems for continuous and discrete variable optimization, particularly nonlinear and mixedinteger nonlinear programming. We also review their extensions to dynamic optimization and optimization under uncertainty. While these areas are still subject to significant research efforts, the emphasis in this paper is on major developments that have taken place over the last twenty five years.
ACADO Toolkit  An OpenSource Framework for Automatic Control and Dynamic Optimization
, 2012
"... ..."
Solving differentialalgebraic equations by Taylor series (ii): Computing the System Jacobian
"... This paper is one of a series underpinning the authors ’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coe ..."
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Cited by 20 (9 self)
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This paper is one of a series underpinning the authors ’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and contain derivatives of order higher than one. Algorithmic details are given. Second, it proves that either the method succeeds in the sense of computing TCs of the local solution, or one of a number of detectable error conditions occurs.
Steering Exact Penalty Methods for Nonlinear Programming
, 2007
"... This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. I ..."
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Cited by 18 (0 self)
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This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods.
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.
Time dependent contamination source determination for water networks. Submitted to A.S.C.E
 Journal of Water Resources Planning and Manag
, 2004
"... Concern about malicious contamination of municipal drinking water networks requires us to consider additional protection measures over physical security alone. In the event of an accidental contamination or malicious attack, knowledge of the time and location of the contamination source can help in ..."
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Cited by 13 (2 self)
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Concern about malicious contamination of municipal drinking water networks requires us to consider additional protection measures over physical security alone. In the event of an accidental contamination or malicious attack, knowledge of the time and location of the contamination source can help infrastructure personnel stop the contamination and propose control strategies for containment or flushing. In this work, we develop a large scale, nonlinear program for identifying contamination sources given concentration measurements from a limited sensor grid installed in the water network. In a previous work [16], we demonstrated the potential for optimization techniques on the contamination source determination problem, but showed that the direct sequential approach was insufficient to solve the fully time dependent problem. In this current work, we use a direct simultaneous approach, converging the network model and optimization problems simultaneously. To obtain reasonable problem sizes, we present an origin tracking algorithm that reformulates the pipe expressions (partial differential equations in time and space) into a system of algebraic expressions in time alone. This algorithm provides a straightforward mathematical representation of the pipe boundary concentrations and is efficient for large networks with many source and output nodes. After reformulating the optimization constraints, we can solve the resulting nonlinear programming problem with large scale optimization tools. The fully time dependent solution gives complete injection profiles, identifying both the time and location of potential sources of contamination. We demonstrate the effectiveness of this formulation on a model for a real municipal water network.
CURVATURE WEIGHTED METRICS ON SHAPE SPACE OF HYPERSURFACES IN nSPACE
"... Abstract. Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the ..."
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Cited by 12 (9 self)
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Abstract. Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape space that are induced by metrics on the space of immersions of the form Gf (h, k) = Φ.¯g(h, k) vol(f