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A decomposition method for structured linear and nonlinear programs

M.D. Grigoriadis, K. Ritter
1969 Journal of computer and system sciences (Print)  
A decomposition method for nonlinear programming problems with structured linear constraints is described.  ...  An algorithm for performing post optimality analysis--ranging and parametric programming--for such structured linear programs is included.  ...  Rosen, and the contribution to certain sections of the decomposition program by Mr. Dennis Kuba.  ... 
doi:10.1016/s0022-0000(69)80026-7 fatcat:znqtfxz33nax7krv5hlmhdwt4i

Page 1915 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
Westerberg, Decomposition methods for solving steady state process design problems (pp. 379-397); Klaus Ritter, A decomposition method for structured nonlinear programming problems (pp. 399-413); Carl-Louis  ...  Grigoriadis, Unified pivoting proce- dures for large structured linear systems and programs (pp. 447- 465); A. K. Kevorkian and J.  ... 

Page 874 of Mathematical Reviews Vol. 45, Issue 3 [page]

1973 Mathematical Reviews  
Grigoriadis, Michael D. 4826 A projective method for structured nonlinear programs. Math. Programming 1 (1971), 321-358.  ...  Decomposition algorithms for solving large structure linear fractional programs, and for parametic linear ECONOMICS, OPERATIONS RESEARCH, PROGRAMMING, GAMES cedure given in the literature.  ... 

Page 5704 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
The KKT systems arising in barrier methods for linear and nonlinear programming are studied, and preconditioners for use with SYMMLQ are de- rived.  ...  After deriving a priori estimates, we evaluate a posteriori estimates using three different methods of minimization, which are linear programming, least squares and a recursive projection algorithm for  ... 

Simple Technique of Projected Lagrange for a Class of Multi-Stage Stochastic Nonlinear Programs

Ihda Hasbiyati, Saib Suwilo
2015 Global Journal of Technology and Optimization  
Since all method is gone upon on special structure of programs characters linear stochastics, so is hard generalisation to solve nonlinear stochastic programs, Gongyun Zhao introduces iterasi's method  ...  Have a lot of research that gets contribution to solve Multi-stage stochastic nonlinear programs amongst those methodics decomposition that is utilized on nonliner's program also linear [1, 2] .  ... 
doi:10.4172/2229-8711.1000179 fatcat:vmlzo5f2gvfnld5jgksitl55pu

Nondifferentiable Optimization and Large Scale Linear Programming [chapter]

Jeremy F. Shapiro
1979 International Symposium on Systems Optimization and Analysis  
This is any linear programming problem with special structure and sufficient size that decomposition methods exploiting the special structure are more efficient than solving the problem by direct methods  ...  Specially structured large scale linear programming problems can also arise as approximations to smaller mathematical programming problems that are not linear such as the convex nonlinear programming problem  ... 
doi:10.1007/978-3-662-39921-7_19 fatcat:cjy62nqbzbcfpbzpcpfmnehgzm

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

Masatoshi Sakawa, Kosuke Kato
2009 Advances in Operations Research  
We focus on multiobjective nonlinear integer programming problems with block-angular structures which are often seen as a mathematical model of large-scale discrete systems optimization.  ...  For deriving a satisficing solution for the decision maker, we develop an interactive fuzzy satisficing method.  ...  One familiar special structure is the block-angular structure to the constraints and several kinds of decomposition methods for linear and nonlinear programming problems with block-angular structure have  ... 
doi:10.1155/2009/372548 fatcat:fn6lkio2ojgxnf4ksl2qnyqima

A nonlinear bilevel model for analysis of electric utility demand-side planning issues

Benjamin F. Hobbs, Sushil K. Nelson
1992 Annals of Operations Research  
An application of bilevel programming in the electric utility industry is presented. The model is nonlinear and is used to analyze various economic issues that affect electric utility planning.  ...  The moders solutions shed light on utility issues including whether there can be a practical difference between various objectives, including minimizing cost ("least cost" planning) and maximizing net  ...  The latter approach is based on embedding the Kuhn-Tucker (KT) conditions for the lower-level problem in a single non-convex mathematical program and solves it by a branch and bound method.  ... 
doi:10.1007/bf02098182 fatcat:42weio2rorhnfh5zkal5zr4lfa

Page 1236 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews  
The following decomposition procedures for such problems are developed: (1) a dynamic programming method, (2) a two-point boundary value problem method, (3) multilevel methods, and (4) the formulation  ...  The author generalizes the Charnes- Cooper method for solving linear fractional programming problems to such problems with unbounded feasible sets. In a previous paper the author and V. M.  ... 

Page 59 of Automation and Remote Control Vol. 35, Issue 5 [page]

1974 Automation and Remote Control  
B, S, Razumikhin, *Iteration method of solution and decomposition of problems of linear programming,* Avtomat, i Telemekhan,, No, 3 (1967), T, N, Pervovanskaya and A, A, Pervozvanskii, * Decentralization  ...  G, Pliskin, "Conditional optimization of a chemical plant," Avtomat, i Telemekhan,, No, 10 (1962), G, B, Dantzig and P, Wolfe, *Decomposition principle for linear programs,* Operat, Res,, 8, No, 1 (1960  ... 

Search Direction Generation via a Proposed Model

Ibrahim Omara
2022 Mathematical Statistician and Engineering Applications  
This study proposes a decomposition method through which they can be a successful solution to multi-stage stochastic nonlinear programs. The proposed method entails the scenario analysis method.  ...  This study's focus is on the efforts seeking to establish a nonlinear programming model targeting problems with much nonlinearity, as well as linear constraints existing in large sparse sets; with the  ...  Given that all the methods rely on stochastic linear programs' special properties and structures, it is imperative to highlight that the generalization of the methods towards solving stochastic nonlinear  ... 
doi:10.17762/msea.v71i1.56 fatcat:7wlk34rxyrc2thwej3qk5nozrm

Genetic Programming for the Identification of Nonlinear Input−Output Models

János Madár, János Abonyi, Ferenc Szeifert
2005 Industrial & Engineering Chemistry Research  
The method uses Genetic Programming (GP) to generate nonlinear input-output models of dynamical systems that are represented in a tree structure.  ...  The simulation results show that the developed tool provides an efficient and fast method for determining the order and the structure for nonlinear input-output models.  ...  This paper proposes such hybridization of Genetic Programming (GP) and the Orthogonal Least Squares (OLS) for the structure selection of nonlinear models that are linear-in-parameters.  ... 
doi:10.1021/ie049626e fatcat:vr6pqwra2vfkfdovhlpollfngu

Linear-in-Parameter Models Based on Parsimonious Genetic Programming Algorithm and Its Application to Aero-Engine Start Modeling

Ying-hong LI, Xun-kai WEI
2006 Chinese Journal of Aeronautics  
In application of this method, first, the traditional Genetic Programming(GP) is used to generate the nonlinear input-output models that are represented in a binary tree structure; then, the Orthogonal  ...  enhance GP's convergence speed; and finally, a simple, reliable and exact linear-in-parameter nonlinear model via GP evolution is obtained.  ...  Conclusions This paper proposes a novel GP algorithm called PGP for nonlinear structure selection of linear-in-parameter models.  ... 
doi:10.1016/s1000-9361(11)60331-2 fatcat:b6c33hcqyfa2tktzb3cbtynkcm

Page 1083 of Mathematical Reviews Vol. 56, Issue 3 [page]

1978 Mathematical Reviews  
Guevski, Hija 8002 A decomposition method for a certain class of nonlinear program- ming problems. (Bulgarian. Russian and English summaries) B"lgar. Akad. Nauk. Izv. Inst. Tehn.  ...  Author’s summary: “A decomposition method, used in least- weight plastic design, is extended to solve problems with non- linearity arising from variable structure geometry.  ... 

Page 460 of American Society of Civil Engineers. Collected Journals Vol. 113, Issue 4 [page]

1987 American Society of Civil Engineers. Collected Journals  
The solution technique developed here for the operation problem is a version of Successive Linear Programming (SLP) and involves the iter- ative solution of a series of linear programming problems, where  ...  The solution procedure for the LP problem is described first, followed by the overall iterative SLP proce- dure. Linear Program Decomposition Procedure.  ... 
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