Advantages of Nonlinear-Programming-Based Methodologies for Inequality Path-Constrained Optimal Control Problems—A Numerical Study

Kameswaran, Shivakumar; Biegler, Lorenz T.

doi:10.1137/050644938

Cited by 33 publications

(18 citation statements)

References 10 publications

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“…Subsequently another group (Kameswaran and Biegler 2005), using a different direct transcription numerical code, solved the same problem and got an answer similar to ours.…”

Section: Introductionsupporting

confidence: 65%

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Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

2007

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Theoretical results from optimal control theory and numerical analysis play an important role in understanding and numerically solving optimal control problems with higher order state inequality constraints. However, the application of these theoretical results to numerical practice can sometimes be misleading. In this paper we examine a specific example which arose in the development of an industrial grade optimal control package that uses a direct transcription approach. This example illustrates several aspects of direct transcription codes that require a reinterpretation of the numerical and analytical theory.

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“…Subsequently another group (Kameswaran and Biegler 2005), using a different direct transcription numerical code, solved the same problem and got an answer similar to ours.…”

Section: Introductionsupporting

confidence: 65%

“…However, we could not solve it with SOCS for N > 4. Subsequently, Kameswaran and Biegler examined the boundary value problem that arises when it is assumed there is a constraint arc and showed that it is very ill-conditioned (Kameswaran and Biegler 2005). However, that does not tell the full story.…”

Section: Computational Studiesmentioning

confidence: 98%

Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

2007

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“…Third, we will discuss the well known benchmark problem by Betts and Campbell from [6,7] that originally motivated our research on parabolic boundary control problems, and, as a first step, the work in [30] on elliptic boundary control problems, and suggest a framework for its analysis. We will use an approximation to this model problem, which has also been investigated in the context of direct transcription methods by Kameswaran and Biegler [16] or Betts et al in [8], for our numerical experiments.…”

Section: Introductionmentioning

confidence: 99%

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Neitzel¹,

Tröltzsch²

2008

ESAIM: COCV

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Abstract. In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.Mathematics Subject Classification. 49K20, 49N10, 49M05.

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“…As discussed in Kameswaran and Biegler [42], these can present some interesting advantages on large-scale problems. Recent work [42][43][44] has shown that simultaneous approaches have distinct advantages for singular control problems and problems with high index path constraints.…”

Section: Simultaneous Gradient-based Approachesmentioning

confidence: 99%

Hybrid Dynamic Optimization Methods for Systems Biology with Efficient Sensitivities

2015

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Abstract:In recent years, model optimization in the field of computational biology has become a prominent area for development of pharmaceutical drugs. The increased amount of experimental data leads to the increase in complexity of proposed models. With increased complexity comes a necessity for computational algorithms that are able to handle the large datasets that are used to fit model parameters. In this study the ability of simultaneous, hybrid simultaneous, and sequential algorithms are tested on two models representative of computational systems biology. The first case models the cells affected by a virus in a population and serves as a benchmark model for the proposed hybrid algorithm. The second model is the ErbB model and shows the ability of the hybrid sequential and simultaneous method to solve large-scale biological models. Post-processing analysis reveals insights into the model formulation that are important for understanding the specific parameter optimization. A parameter sensitivity analysis reveals shortcomings and difficulties in the ErbB model parameter optimization due to the model formulation rather than the solver capacity. Suggested methods are model reformulation to improve input-to-output model linearity, sensitivity ranking, and choice of solver.

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Advantages of Nonlinear-Programming-Based Methodologies for Inequality Path-Constrained Optimal Control Problems—A Numerical Study

Cited by 33 publications

References 10 publications

Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Hybrid Dynamic Optimization Methods for Systems Biology with Efficient Sensitivities

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