Nonlinear Function Minimization Research Articles

A class of descent algorithms for nonlinear function minimization with linear equality constraints

We consider the application of the ABS algorithms, introduced by [I], mainly for the solution of linear algebraic systems, to constrained optimization problems with equality constraints. A general formulation of feasible direction algorithms is obtained and the ABS formulation is given of the reduced gradient method of Wolfe (1967) and of the projected gradient method of Rosen (1960)

Vectorization of conjugate-gradient methods for large-scale minimization in meteorology

During the last few years, conjugate-gradient methods have been found to be the best available tool for large-scale minimization of nonlinear functions occurring in geophysical applications. While vectorization techniques have been applied to linear conjugate-gradient methods designed to solve symmetric linear systems of algebraic equations, arising mainly from discretization of elliptic partial differential equations, due to their suitability for vector or parallel processing, no such effort was undertaken for the nonlinear conjugate-gradient method for large-scale unconstrained minimization.

Determination of Fish Movement Patterns from Tag Recoveries using Maximum Likelihood Estimators

A general method for analysis of movement data from tag returns is proposed which has four major components: (1) a population dynamics and movement model that describes how the number of tagged individuals in each spatial location changes over time; (2) an observation model which describes how the tags are recovered and reported; (3) a likelihood function that specifies the likelihood of observing a specific number of recoveries in each space/time stratum as a function of the number thought to be there under a specific set of parameters of the population dynamics, movement and observation models, and (4) a nonlinear function minimization computer algorithm. This approach is applied to movements of skipjack tuna (Euthynnus pelamis). When tagging and recapture take place in each spatial stratum, reliable estimates of movement rates can be obtained. The approach described is completely general and can be used in cases where movement takes place continuously, or only once in the life history. Methods for determining confidence limits and evaluation of residuals are presented and extensions that include tagging mortality, tag shedding, and size specific vulnerability are discussed.

On the variable mesh finite element analysis of unconfined seepage problems

Some drawbacks affecting the variable mesh finite element solution of unconfined flow problems are discussed and a procedure is suggested aimed at avoiding them in steady state and transient analyses. In particular, it is shown that the results of standard algorithms often used in practice may present spurious oscillations of the phreatic surface in the vicinity of the intersection with a pervious boundary exposed to the atmosphere. They may become exceedingly large when a limited number of elements is adopted in the mesh, and in some cases lead to non-correct final (steady state) configurations of the free surface. In order to eliminate this negative effect from the finite element analysis, a simple criterion is suggested based on an algorithm for non-linear function minimization. Some applications of this technique are presented to two- and three-dimensional unconfined problems. L'article discute la solution à éléments finis de mailles variables des problèmes d'ecoulement sans contrainte latérale et propose une procèdure pour éliminer ses inconvenients dans les analyses sta-tionnaires et transitoires. En particulier on dé-montre que les résultats des algorithmes normaux souvent employés en pratique peuvent faire apparaitre des oscillations fausses de la surface phreatique dans le voisinage de l'intersection avec une limite perméable exposée à l'atmosphère. Ces oscillations tendent à devenir excessives lorsque la maille comprend un nombre limite d'éléments, de sorte qu'on obtient parfois des configurations finales (stationnaires) de la surface libre qui sont incorrectes. Pour éliminer cet effet négatif des analyses avec éléments finis, Particle propose un critère très simple basé sur un algorithms pour la minimalisation fonctionnelle non-linéaire. Des exemples sont donnés de l'application de cette technique aux problèmes bidimensionnels et tridi-mensionnels sans contrainte latérale.

Numerical methods of minimization of nonlinear functions on disjoint simplices

Numerical methods of minimization of nonlinear functions on disjoint simplices

Algorithms for Constrained Minimization of Smooth Nonlinear Functions: Mathematical Programming Study 16

Algorithms for Constrained Minimization of Smooth Nonlinear Functions: Mathematical Programming Study 16

Algorithms for Constrained Minimization of Smooth Nonlinear Functions: Mathematical Programming Study 16

Algorithms for Constrained Minimization of Smooth Nonlinear Functions: Mathematical Programming Study 16

Nonlinear programming on a microcomputer

AbstractThe Davidon‐Fletcher‐Powell (DFP) algorithm for multivariable unconstrained nonlinear function minimization is implemented on a desk microcomputer—the Hindustan Computers MICRO‐2200—with a floppy disk memory extension peripheral. The program is developed using the programming keys of the system. The program is closely based on FMFP, a well‐known FORTRAN subroutine of the algorithm. Among the exercises performed are two standard nonlinear programming (NLP) test problems, namely the Rosenbrock and Wood function minimization and two SUMT (Sequential Unconstrained Minimization Technique) illustration problems in structural optimization, i.e. two‐bar and three‐bar truss weight minimization examples. Experience bears out the potential of desk calculating systems as tools in nonlinear programming algorithm research. Also, the small‐scale structural optimization capability afforded by such systems is expected to be of significance in teaching and preliminary design contexts.

Pharmacokinetics of adriamycin in patients with breast cancer: Correlation between pharmacokinetic parameters and clinical short-term response

The pharmacokinetics of adriamycin was evaluated in the plasma of 12 patients with breast cancer after injection of an i.v. bolus. The patients were suffering from a locally advanced tumor, were free of metastases and had received no prior treatment. They received a chemotherapy consisting in adriamycin (50 mg/ m 2) on day 1, vincristine (1 mg/ m 2) on day 2 and methotrexate (6 mg/ m 2) on days 3, 4 and 5. The response to chemotherapy was assessed as the percentage of reduction of the palpable tumoral mass. Plasma samples were collected at various times after injection of the drug. Adriamycin and its metabolites were extracted using an original column purification technique and were evaluated by high-performance liquid chromatography with fluorometric detection. Pharmacokinetic parameters were calculated with a computer program based upon an algorithm of non-linear function minimization. The three successive half-lives presented little individual variations and were 4.75 min, 0.822 hr and 18.9 hr. On the other hand, the A, B and C parameters were highly scattered. The total plasma clearance of the parent drug ranged from 28.3 to 98.7 l/hr. A highly significant correlation was observed between parameter A and the short-term clinical response. Moreover, a mild correlation exists between the half-life of the 1st phase and the short-term clinical response. We can therefore assume that the efficacy of the drug may be dependent upon its distribution in the organism. Such a relationship may allow the development of new protocols of chemotherapy in order to obtain an optimal distribution of the drug in every patient.

An assessment of quasi-newton sparse update techniques for nonlinear structural analysis

In this paper an attempt is made to evaluate the performance of a few algorithms for unconstrained minimization of nonlinear functions that exploit sparsity of the Hessians of such functions. The evaluation is centered around large scale, geometrically nonlinear problems of structural analysis in general. In particular, the snap-through response of finite element models of a shallow elastic arch under a concentrated load at the crown is considered. The sensitivity of these algorithms to varying degrees of refinement of these finite element models as well as to the sparsity pattern of the Hessian of the potential surface in question are examined. The paper concludes by making recommendations on the choice of an algorithm based on the scale of the problem and the degree and type of nonlinearity.

Minimization of nonlinear functionals for constrained problems

Minimization of nonlinear functionals for constrained problems

State Estimation of Large Scale Electric Power Systems by Decomposition Methods

This paper deals with the computational methods for the state estimation problem of a large-Scale electric Power system. This state estimation problem can be defined as the power flow problem which has overdetermined boundary conditions, and non-linear function minimization techniques can be used to solve the problem. The mathematical foundation of proposed methods is based upon the perturbed Newton method which includes as special cases standerd function minimization techniques such as Newton-Gauss method, Fretcher-Powel1 method and steerest descent method.The proposed methods in this paper are considered as decomposition methods for the reason that the coefficient matrices of iteration schemes are decomposed into block diagonal forms from the view joints of a power system configuration or a sersitivity between variab1es.These methods are suitable for the state-estimation problem which has many state variables for the simplicity of the coefficient moatrix in non-linear function minimization techniques.

Minimization of non‐linear separable convex functionals

Naval Research Logistics QuarterlyVolume 1, Issue 4 p. 301-312 Article Minimization of non-linear separable convex functionals† A. Charnes, A. Charnes Carnegie Institute of TechnologySearch for more papers by this authorC. E. Lemke, C. E. Lemke General Electric CompanySearch for more papers by this author A. Charnes, A. Charnes Carnegie Institute of TechnologySearch for more papers by this authorC. E. Lemke, C. E. Lemke General Electric CompanySearch for more papers by this author First published: December 1954 https://doi.org/10.1002/nav.3800010408Citations: 54 † This paper was written as part of the project, “The Planning and Control of Industrial Operations” under Contract Nonr-760(01) with the Office of Naval Research. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume1, Issue4December 1954Pages 301-312 RelatedInformation