Applied hybrid system optimization: An empirical investigation of complexity

Till, Jochen; Engell, Sebastian; Panek, Sebastian; Stursberg, Olaf

doi:10.1016/j.conengprac.2004.04.003

Cited by 60 publications

(32 citation statements)

References 34 publications

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“…Therefore MINLP techniques will work only on limited and small time horizons because of the exponentially growing complexity of the problem, [45].…”

Section: Mi(n)lp Algorithmsmentioning

confidence: 99%

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

Säger

2009

Journal of Process Control

121

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“…Therefore MINLP techniques will work only on limited and small time horizons because of the exponentially growing complexity of the problem, [45].…”

Section: Mi(n)lp Algorithmsmentioning

confidence: 99%

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

Säger

2009

Journal of Process Control

121

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“…Therein, Z i R i = 0 and Y i R i = R R i Thus (19) can be solved for δ λ i once δ w i and δ λ i−1 are known, while (20) can be used to determine the point constraints multipliers δ µ i . Let thus null space projections be defined as follows:…”

Section: Hessian Projectionmentioning

confidence: 99%

“…The full primal step δ w is then obtained from δ w = Y δ w Y + Zδ w Z . The constraint multipliers step δ µ is recovered using (20).…”

Section: Hessian Projectionmentioning

confidence: 99%

See 1 more Smart Citation

Complementary Condensing for the Direct Multiple Shooting Method

Kirches

Bock

Schlöder

et al. 2012

Modeling, Simulation and Optimization of Complex Processes

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Summary. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning the solution of the quadratic subproblems we present a factorization of the QP's KKT system, based on a combined null-space range-space approach exploiting the problem's block sparse structure. We demonstrate the merit of this approach for a vehicle control problem in which the integer gear decision is convexified.

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“…The drawback of direct methods with binary control functions obviously is that they lead to high-dimensional vectors of binary variables. Because of the exponentially growing complexity of the problem, techniques from mixed-integer nonlinear programming will work only for small instances [37]. In past contributions [23,29,30,33] we proposed to use an outer convexification with respect to the binary controls, which has several main advantages over standard formulations or convexifications, cf.…”

Section: Introductionmentioning

confidence: 99%

Block-structured quadratic programming for the direct multiple shooting method for optimal control

Kirches

Bock

Schlöder

et al. 2011

Optimization Methods and Software

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Abstract. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using sequential quadratic programming methods. We review the classical condensing algorithm that preprocesses the large but sparse quadratic programs to obtain small but dense ones. We show that this approach leaves room for improvement when applied in conjunction with outer convexification. To this end, we present a new complementary condensing algorithm for quadratic programs with many controls. This algorithm is based on a hybrid null-space range-space approach to exploit the block sparse structure of the quadratic programs that is due to direct multiple shooting. An assessment of the theoretical run time complexity reveals significant advantages of the proposed algorithm. We give a detailed account on the required number of floating point operations, depending on the process dimensions. Finally we demonstrate the merit of the new complementary condensing approach by comparing the behavior of both methods for a vehicle control problem in which the integer gear decision is convexified.

show abstract

Applied hybrid system optimization: An empirical investigation of complexity

Cited by 60 publications

References 34 publications

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

Complementary Condensing for the Direct Multiple Shooting Method

Block-structured quadratic programming for the direct multiple shooting method for optimal control

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