NON-LINEAR OPTIMIZATION AND LARGE-SCALE PROBLEMS

1991 ◽  
Vol 18 (1-3) ◽  
pp. 5-21 ◽  
Author(s):  
J. C. GILBERT
Keyword(s):  
Large Scale ◽  
Linear Optimization ◽  
Large Scale Problems ◽  
Non Linear

COMBINING FLUX AND ENERGY BALANCE ANALYSIS TO MODEL LARGE-SCALE BIOCHEMICAL NETWORKS

2006 ◽  
Vol 04 (06) ◽  
pp. 1227-1243 ◽  
Author(s):  
WILLIAM J. HEUETT ◽  
HONG QIAN
Keyword(s):  
Energy Balance ◽  
Large Scale ◽  
Heat Dissipation ◽  
Linear Optimization ◽  
Biochemical Networks ◽  
Programming Algorithm ◽  
Optimization Approach ◽  
Stoichiometric Matrix ◽  
Non Linear ◽  
Detailed Kinetics

Stoichiometric Network Theory is a constraints-based, optimization approach for quantitative analysis of the phenotypes of large-scale biochemical networks that avoids the use of detailed kinetics. This approach uses the reaction stoichiometric matrix in conjunction with constraints provided by flux balance and energy balance to guarantee mass conserved and thermodynamically allowable predictions. However, the flux and energy balance constraints have not been effectively applied simultaneously on the genome scale because optimization under the combined constraints is non-linear. In this paper, a sequential quadratic programming algorithm that solves the non-linear optimization problem is introduced. A simple example and the system of fermentation in Saccharomyces cerevisiae are used to illustrate the new method. The algorithm allows the use of non-linear objective functions. As a result, we suggest a novel optimization with respect to the heat dissipation rate of a system. We also emphasize the importance of incorporating interactions between a model network and its surroundings.

scholarly journals VIMO: A Visual-Inertial-Magnetic Navigation System Based on Non-Linear Optimization

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4386
Author(s):  
Jingzhe Wang ◽  
Leilei Li ◽  
Huan Yu ◽  
Xunya Gui ◽  
Zucheng Li
Keyword(s):  
Large Scale ◽  
Linear Optimization ◽  
Position Estimation ◽  
Measurement Unit ◽  
Navigation Systems ◽  
Non Linear ◽  
Outdoor Environments ◽  
Novel Method ◽  
And Performance ◽  
Inertial Measurements

Visual-inertial navigation systems are credited with superiority over both pure visual approaches and filtering ones. In spite of the high precision many state-of-the-art schemes have attained, yaw remains unobservable in those systems all the same. More accurate yaw estimation not only means more accurate attitude calculation but also leads to better position estimation. This paper presents a novel scheme that combines visual and inertial measurements as well as magnetic information for suppressing deviation in yaw. A novel method for initializing visual-inertial-magnetic odometers, which recovers the directions of magnetic north and gravity, the visual scalar factor, inertial measurement unit (IMU) biases etc., has been conceived, implemented, and validated. Based on non-linear optimization, a magnetometer cost function is incorporated into the overall optimization objective function as a yawing constraint among others. We have done extensive research and collected several datasets recorded in large-scale outdoor environments to certify the proposed system’s viability, robustness, and performance. Cogent experiments and quantitative comparisons corroborate the merits of the proposed scheme and the desired effect of the involvement of magnetic information on the overall performance.

Designing optimal universal pulses using second-order, large-scale, non-linear optimization

2012 ◽  
Vol 219 ◽  
pp. 61-74 ◽  
Author(s):  
Christopher Kumar Anand ◽  
Alex D. Bain ◽  
Andrew Thomas Curtis ◽  
Zhenghua Nie
Keyword(s):  
Large Scale ◽  
Linear Optimization ◽  
Second Order ◽  
Non Linear

scholarly journals Solveurs multigrilles et méthode asymptotique numérique

2007 ◽  
pp. 813-826
Author(s):  
Anas Mtalaa ◽  
Jean-Marc Cadou ◽  
Michel Potier-Ferry
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Large Scale ◽  
Perturbation Technique ◽  
The Finite Element Method ◽  
Numerical Techniques ◽  
Asymptotic Numerical Method ◽  
Large Scale Problems ◽  
Non Linear

The aim of this work is to build up new numerical techniques to solve non-linear large scale problems. We propose to couple multigrid techniques with the asymptotic numerical method (ANM) which associates a perturbation technique with the finite element method.

The Use of Decomposition for the Large Scale Synthesis/Design Optimization of Highly Coupled, Highly Dynamic Energy Systems: Part II—Applications

2000 ◽  
Author(s):  
Jules R. Muñoz ◽  
Michael R. von Spakovsky
Keyword(s):  
Global Convergence ◽  
Design Optimization ◽  
Large Scale ◽  
Environmental Control ◽  
Linear Optimization ◽  
Mixed Integer ◽  
Decomposition Approach ◽  
Independent Variables ◽  
Synthesis Design ◽  
Non Linear

Abstract An application of the Iterative Local-Global Optimization (ILGO) decomposition approach developed in an accompanying paper (Muñoz and von Spakovsky, 2000b) is presented. The synthesis / design optimization of a turbofan engine coupled to an environmental control system for a military aircraft was carried out. The problem was solved for a given mission (i.e. the load / environmental profile) composed of fifteen segments. The number of decision (independent) variables used for this highly non-linear optimization problem is one hundred fifty-three, some of which are integer. Both thermodynamic and physical (weight and volume) simulations use state-of-the art tools. Two objective functions were investigated: take-off gross weight and mission fuel consumption, and no observable differences were found in the final results. In addition to the mathematical foundations for global convergence of the proposed decomposition approach presented in Muñoz and von Spakovsky (2000b), numerical support for this convergence was found by solving the entire mixed-integer non-linear programming (MINLP) problem without decomposition using a subset of the independent variables. The constant value of the marginal costs (or linear behavior of the Optimum Response Surface — OSR) played a major role in the global convergence of the ILGO.

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