Comparison of optimization algorithms

Jones, D. I.; Finch, J.W.

doi:10.1080/00207178408933304

Cited by 34 publications

(14 citation statements)

References 16 publications

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“…in the non-negative orthant. For instance, in [ U ] a steplengtha is determined so that for Algorithm 1: (29) and for Algorithm 2: p ( a ) = p , + a ( A p " + h p ' ) +~~~A p~* (30) where we define p T = [xr,h7,vT,sT J along with similar notation for related terms. Using the less restrictive guidelines of [85], the largest steplength & E (OJ] is chosen that satisfies:…”

Section: Ip Methods Within Sqpmentioning

confidence: 99%

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Large scale inequality constrained optimization and control

Gopal

Biegler²

1998

IEEE Control Syst.

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S methods in linear programming have triggered a tremendous amount of activity. The applicability of interior point methods for the efficient solution of nonlinear programming problems has also been of interest, and has shown huge potential benefits. This has tremendous impact in process control, especially since optimal control and model predictive control problems, hitherto coiisidered unsolvable, could be solved in a realistic time. In this article, we outline some recent developments in interior point methods for the solution of linear and nonlinear programming problems followed by a summary of the recent work for applying these concepts in control. We conclude with a review of current status and a discussion of future directions. Linear and Nonlinear Programming Linear programming (LP) problems have been formulated and solved in diverse disciplines as engineering, economics and sociology since the 1930s. An LP consists of an objective function, equality and inequality constraints, all ofwhich are linear in the vector of real variables. A general linear programming problem can be formulated as Min c ' x s. t. Ax = h x 2 0 .

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Section: Ip Methods Within Sqpmentioning

confidence: 99%

“…Any of single shooting, multiple shooting, and global methods are used for the solution of the BVP (see Bryson and Ho [12] for details). The indirect method works well for unconstrained problems, but the presence of inequalities in the model poses difficulties for these methods (Jones and Finch [30], Ray [65]).…”

Section: Control and Optimizationmentioning

confidence: 99%

Large scale inequality constrained optimization and control

Gopal

Biegler²

1998

IEEE Control Syst.

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“…The sequential solution and optimization requires the solution of differential equations at each iteration of the optimization. Jones and Finch (1984) found that such methods spend about 85% of the time integrating the model equations in order to obtain gradient information. This can make the implementation of this algorithm computationally expensive for cases involving a large number of model equations.…”

Section: Sequential Solution and Optimization Algorithmmentioning

confidence: 99%

Nonlinear model predictive control of a reactive distillation column

Kawathekar

2007

Control Engineering Practice

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This paper considers the application of nonlinear model predictive control (NLMPC) to a highly nonlinear reactive distillation column. NLMPC was applied as a nonlinear programming problem using orthogonal collocation on finite elements to approximate the ODEs that constitute the model equations for the reactive distillation column. Diagonal PI controls were used to identify that the [L/D,V] and the [L/D,V/B] configurations performed best. NLMPC was applied using the [L/D,V] configuration and found to provide a factor of 2-3 better performance than the corresponding PI controller. The effect of process/model mismatch on the performance of the NLMPC controller was also evaluated. r

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“…A subroutine is used for numerical integration of the state equations. A comparison of several CVI algorithms is given in [Jones84] and an extensive theoretical treatment can be found in [Goh88]. An alternative approach to CVI is iterative dynamic programming (IDP) , which relies on forward integration of the state equations, discretization of possible values of u(t) over a region and subsequent repeated region contraction [Luus93a,Luus93b].…”

Section: Piecewise Constant or Piecewise Linear U(t)mentioning

confidence: 99%