Optimum sensitivity derivatives of objective functions in nonlinear programming

AIAA Journal ◽  
1983 ◽  
Vol 21 (6) ◽  
pp. 913-915 ◽  
Author(s):  
Jean-Francois M. Barthelemy ◽  
Jaroslaw Sobieszczanski-Sobieski
Keyword(s):  
Nonlinear Programming ◽  
Objective Functions ◽  
Sensitivity Derivatives ◽  
Derivatives Of

scholarly journals Extended Duality in Fuzzy Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Tingting Zou
Keyword(s):  
Nonlinear Programming ◽  
Original Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Duality Gap ◽  
Continuous Variables ◽  
Objective Functions ◽  
Duality Theorems ◽  
Fuzzy Nonlinear Programming

Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.

scholarly journals Adjoint-Based Aerodynamic Design of Complex Aerospace Configurations

2016 ◽  
Author(s):  
Eric J. Nielsen
Keyword(s):  
Large Scale ◽  
Design Research ◽  
Design Parameters ◽  
Aerodynamic Design ◽  
Cfd Simulations ◽  
Sensitivity Derivatives ◽  
Computational Fluid Dynamics Cfd ◽  
Langley Research Center ◽  
The Cost ◽  
Derivatives Of

An overview of twenty years of adjoint-based aerodynamic design research at NASA Langley Research Center is presented. Adjoint-based algorithms provide a powerful tool for efficient sensitivity analysis of complex large-scale computational fluid dynamics (CFD) simulations. Unlike alternative approaches for which computational expense generally scales with the number of design parameters, adjoint techniques yield sensitivity derivatives of a simulation output with respect to all input parameters at the cost of a single additional simulation. With modern large-scale CFD applications often requiring millions of compute hours for a single analysis, the efficiency afforded by adjoint methods is critical in realizing a computationally tractable design optimization capability for such applications.

scholarly journals OPTIMAL DESIGN OF BOREHOLES TRAJECTORIES

2021 ◽  
Vol 1 (48) ◽  
pp. 109-116
Author(s):  
Gulyayev V ◽  
◽  
Shlyun N ◽  
Keyword(s):  
Optimal Control ◽  
Nonlinear Programming ◽  
Trajectory Optimization ◽  
Oil And Gas ◽  
Total Curvature ◽  
Objective Functions ◽  
Gas Wells ◽  
Well Trajectory ◽  
Complex Constraints ◽  
First Time

The problem of optimizing the trajectories of deep curved oil and gas wells, in which the total curvature of the well and its length is minimized, is discussed. For the first time, a discrete-continuum model of the well geometry was proposed, based on the method of projection of a gradient on the hyperplane of linearized constraints, a method was developed for minimizing the corresponding target functionals, which would reduce the risks of emergency drilling situations. An algorithm for reducing the problem of nonlinear optimal control to the problem of nonlinear programming is shown. Such a transition is achieved by approximating the well trajectories with a system of cubic splines, analytically integrating differential equations in separate sections of the trajectory, and further applying the methods of nonlinear programming theory. The considered approach is more algorithmic and allows solving problems of well trajectory optimization under more complex constraints. KEYWORDS: WELL TRACKING, OPTIMAL CONTROL PROBLEM, OBJECTIVE FUNCTIONS, NONLINEAR PROGRAMMING.

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