A fast algorithm for nonlinearly constrained optimization calculations

Powell, M. J. D.

doi:10.1007/bfb0067703

Cited by 1,154 publications

(634 citation statements)

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“…IfĤ k−1 is positive semidefinite, the BFGS update with the above condition can be suitably damped such thatĤ k is also positive semidefinite; see, e.g., [29]. At each iteration of the SSP method, problem (30) is solved with H k replaced by the matrixĤ k that is obtained by the BFGS update ofĤ k−1 from the previous SSP iteration.…”

Section: An Ssp Methods For Nonlinear Semidefinite Programsmentioning

confidence: 99%

“…A proof of convergence for such modifications is the subject of current research; see, e.g., [10]. Since all the data enters in a continuous fashion in the preceding analysis, it follows that the SSP method with step size one is still locally superlinearly convergent if the matrices H k in (29) are replaced by approximationsĤ k with H k −Ĥ k → 0.…”

Section: Theorem 3 Assume That the Functionmentioning

confidence: 99%

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Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling

2006

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We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more complicated than the solution of standard nonlinear programs. This paper studies a sequential semidefinite programming (SSP) method, which is a generalization of the well-known SQP method for standard nonlinear programs. We present a sensitivity result for nonlinear semidefinite programs, and then based on this result, we give a self-contained proof of local quadratic convergence of the SSP method. We also describe a class of nonlinear semidefinite programs that arise in passive reduced-order modeling, and we report results of some numerical experiments with the SSP method applied to problems in that class.

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Section: An Ssp Methods For Nonlinear Semidefinite Programsmentioning

confidence: 99%

Section: Theorem 3 Assume That the Functionmentioning

confidence: 99%

Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling

2006

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“…functional gradients are calculated numerically. The routine is based on the version of the conjugate gradient algorithm described in Powell (1977Powell ( , 1978. The main advantage of the conjugate gradient technique is that it provides a fast rate of convergence without the storage of any matrices.…”

Section: Optimizationmentioning

confidence: 99%

The structural porosity in soil hydraulic functions - a review

Kutílek¹,

Jendele²

2008

Soil & Water Res.

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Products of biological processes are the dominant factor of soil structure formation in A horizons, while in B horizons their role is less expressed. Soil structure influences dominantly the structural domain of the pore system in bimodal soils thus affecting soil hydraulic functions. The form of soil hydraulic functions depends upon the pore size distribution and generally upon configuration of the soil pore system. We used the functions derived for the lognormal pore size distribution and modified them to bi-modal soils. The derived equations were tested by experimental data of catalogued soils. The procedure leads to the separation of two mutually different domains of structural and matrix pores. The value of the pressure head (potential) separating the two domains is not constant and varies in a broad range. For each domain we obtained its water retention function and unsaturated hydraulic conductivity function. The separation of hydraulic functions for the two domains is a key problem in the solution of preferential flow and in controlling lateral flow between the structural and matrix domains. Water retention function is fully physically based while the conductivity function still keeps fitting parameters, too. Their simple relationship to tortuosity and pores connectivity was not confirmed. Since they differ substantially for matrix and structural domains, we suppose that there exists a great difference in configuration of porous systems in structural and matrix domains. The use of uniform fitting conductivity parameters for the whole range of pores is not justifiable.

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“…Hence, the objective fimetion (48) is an approximation of the original objective funetion (38). The equality constraints (49) are the collocation conditions (47) . The inequalities (50) and the right inequality of (51) reflect the constraints (40) and (41) of the original problem.…”

Section: Breinbauer and P Lorymentioning

confidence: 99%

The kidney model as an inverse problem

Breinbauer¹,

Lory

1991

Applied Mathematics and Computation

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The mammalian kidney is modeled by a multipoint boundary-value problem for a System of nonlinear ordinary differential equations. A corresponding inverse problem is presented, which allows the rigorous judgement of the potential of the given modeling technique. For its numerical Solution a discretization is proposed, which is tailor-made for kidney models. It leads to a nonlinear-programming problem with nonlinear equality and inequality constraints. The suggested methods are applied to current research problems in renal physiology.

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A fast algorithm for nonlinearly constrained optimization calculations

Cited by 1,154 publications

References 7 publications

Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling

Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling

The structural porosity in soil hydraulic functions - a review

The kidney model as an inverse problem

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