Solving Nonlinear Programming Problems with Stochastic Objective Functions

1972 ◽  
Vol 7 (3) ◽  
pp. 1809 ◽  
Author(s):  
William T. Ziemba
Keyword(s):  
Nonlinear Programming ◽  
Objective Functions

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.

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 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.

A study of uncertain multi-objective nonlinear programming problems for rough intervals

2022 ◽  
pp. 1-15
Author(s):  
E. Ammar ◽  
A. Al-Asfar
Keyword(s):  
Nonlinear Programming ◽  
Nonlinear Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Weighting Method ◽  
Upper Approximation ◽  
Multi Objective ◽  
Inaccurate Data ◽  
Decision Variables ◽  
Rough Interval

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

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