Numerical Optimization Methods in Econometrics

2003 ◽  
pp. 287-328 ◽  
Author(s):  
Lenka Čížková
Keyword(s):  
Numerical Optimization ◽  
Optimization Methods

Nonsmooth Optimization Method for Image Restoration

1995 ◽  
Author(s):  
Kazufumi Ito ◽  
Karl Kunisch
Keyword(s):  
Image Restoration ◽  
Nonsmooth Optimization ◽  
Numerical Optimization ◽  
Augmented Lagrangian ◽  
Energy Criterion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Augmented Lagrangian Methods ◽  
Active Set ◽  
First Order

Abstract In this paper we discuss applications of the numerical optimization methods for nonsmooth optimization, developed in [IK1] for the variational formulation of image restoration problems involving bounded variation type energy criterion. The Uzawa’s algorithm, first order augmented Lagrangian methods and Newton-like update using the active set strategy are described.

The Complementary Roles of Symbolic Computing and Numerical Optimization in Engineering Design Software

1987 ◽  
Author(s):  
R. Ellsworth ◽  
A. Parkinson ◽  
F. Cain
Keyword(s):  
Expert System ◽  
Engineering Design ◽  
Numerical Optimization ◽  
Optimization Methods ◽  
Design Rule ◽  
Rule Base ◽  
Design Problems ◽  
Symbolic Computing ◽  
Engineering Design Problems ◽  
Trial And Error Method

Abstract In many engineering design problems, the designer converges upon a good design by iteratively evaluating a mathematical model of the design problem. The trial-and-error method used by the designer to converge upon a solution may be complex and difficult to capture in an expert system. It is suggested that in many cases, the design rule base could be made significantly smaller and more maintainable by using numerical optimization methods to identify the best design. The expert system is then used to define the optimization problem and interpret the solution, as well as to apply the true heuristics to the problem. An example of such an expert system is presented for the design of a valve anti-cavitation device. Because of the capabilities provided by the optimization software, the expert system has been able to outperform the expert in the test cases evaluated so far.

Model-Based Actuator Trajectories Optimization for a Diesel Engine Using a Direct Method

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Michael Benz ◽  
Markus Hehn ◽  
Christopher H. Onder ◽  
Lino Guzzella
Keyword(s):  
Numerical Optimization ◽  
Fuel Injection ◽  
Direct Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Mean Value ◽  
Pollutant Emissions ◽  
Pollutant Emission ◽  
Transient Operation ◽  
Engine Model

This paper proposes a novel optimization method that allows a reduction in the pollutant emission of diesel engines during transient operation. The key idea is to synthesize optimal actuator commands using reliable models of the engine system and powerful numerical optimization methods. The engine model includes a mean-value engine model for the dynamics of the gas paths, including the turbocharger of the fuel injection, and of the torque generation. The pollutant formation is modeled using an extended quasi-static modeling approach. The optimization substantially changes the input signals, such that the engine model is enabled to extrapolate all relevant outputs beyond the regular operating area. A feedforward controller for the injected fuel mass is used to eliminate the nonlinear path constraints during the optimization. The model is validated using experimental data obtained on a transient engine test bench. A direct single shooting method is found to be most effective for the numerical optimization. The results show a significant potential for reducing the pollutant emissions during transient operation of the engine. The optimized input trajectories derived assist the design of sophisticated engine control systems.

Guidance Performance Benchmarking for Autonomous Rotorcraft

2014 ◽  
Vol 59 (4) ◽  
pp. 1-16 ◽  
Author(s):  
Bérénice Mettler ◽  
Zhaodan Kong ◽  
Chad Goerzen ◽  
Matthew Whalley
Keyword(s):  
Trajectory Optimization ◽  
Numerical Optimization ◽  
Performance Metrics ◽  
Optimization Methods ◽  
Urban Environments ◽  
Performance Benchmarking ◽  
Digital Terrain ◽  
Motion Primitive ◽  
Terrain Elevation ◽  
Methods Numerical

This paper describes a framework for performance evaluation of autonomous guidance systems. The elements of the framework consist of a set of spatial geometries, flight tasks, performance metrics, a flightdynamic model, and baseline solutions. The spatial benchmarks consist of six tasks in simple geometrical environments and 10 tasks in more complex urban environments based on a real digital terrain elevation map. The framework also includes a set of performance metrics used to compare trajectories. The performance baselines used in the proposed framework are near-optimal solutions computed using one of two trajectory optimization methods: numerical optimization based on nonlinear programming for the simple geometric environments and a motion primitive automaton for problems involving the urban environments. The paper concludes with a demonstration of the benchmarking framework using the Obstacle Field Navigation system developed by the Army Aeroflightdynamics Directorate.

scholarly journals An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Lihong Guo ◽  
Gai-Ge Wang ◽  
Heqi Wang ◽  
Dinan Wang
Keyword(s):  
Numerical Optimization ◽  
Firefly Algorithm ◽  
Harmony Search ◽  
Optimization Methods ◽  
Convergence Speed ◽  
Function Optimization ◽  
Global Numerical Optimization ◽  
Running Time ◽  
Hybrid Metaheuristic ◽  
Better Than

A hybrid metaheuristic approach by hybridizing harmony search (HS) and firefly algorithm (FA), namely, HS/FA, is proposed to solve function optimization. In HS/FA, the exploration of HS and the exploitation of FA are fully exerted, so HS/FA has a faster convergence speed than HS and FA. Also, top fireflies scheme is introduced to reduce running time, and HS is utilized to mutate between fireflies when updating fireflies. The HS/FA method is verified by various benchmarks. From the experiments, the implementation of HS/FA is better than the standard FA and other eight optimization methods.

Runner System Balancing for Injection Molds Using Approximation Concepts and Numerical Optimization

1992 ◽  
Author(s):  
Rohinton K. Irani ◽  
Srinivas Kodiyalam ◽  
David O. Kazmer
Keyword(s):  
Numerical Optimization ◽  
Optimization Methods ◽  
Computational Effort ◽  
Automated System ◽  
Injection Mold ◽  
Discrete Variable ◽  
Part Quality ◽  
Filling Simulation ◽  
Variable Problem ◽  
Approximation Concepts

Abstract The goal during runner balancing is to vary the diameters of the runner segments such that all the cavities, in a multi-cavity injection mold, fill at the same time. If the runner system is unbalanced, some cavities will fill before others, begin to overpack, and result in material wastage and inconsistent part quality. Numerical optimization methods and finite element mold-filling simulation are used to solve this nonlinear discrete variable problem. Approximation concepts are used to reduce the computational effort required for solving this iterative problem. This automated system has been successfully tested on a number of family molds.

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