Optimization of Constrained Dynamic Systems Using the Sequential Unconstrained Minimization Technique

1972 ◽  
Vol 94 (4) ◽  
pp. 319-322 ◽  
Author(s):  
B. N. Murali ◽  
L. R. Ebbesen ◽  
H. R. Sebesta
Keyword(s):  
Nonlinear Programming ◽  
Dynamic Systems ◽  
Optimization Problem ◽  
State Constraints ◽  
Unconstrained Minimization ◽  
Terminal State ◽  
Analysis Tool ◽  
Minimization Technique ◽  
Algebraic Optimization ◽  
Nonlinear Programming Method

The development of a computer program for the optimization of dynamic systems subject to parameter and terminal state constraints is presented in this paper. The problem is handled by converting it to an equivalent algebraic optimization problem. The resulting problem is then solved by a modified version (D YS UMT) of the nonlinear programming method S UMT (Sequential Unconstrained Minimization Technique). The available program provides an efficient and convenient analysis tool to aid engineers in the modeling and designing of dynamic systems.

Modification of Nonlinear Equality Constraints in Nonlinear Problems

1974 ◽  
Vol 96 (1) ◽  
pp. 138-144
Author(s):  
R. J. Polo ◽  
V. A. Sposito ◽  
T. T. Lee
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Nonlinear Problems ◽  
Unconstrained Minimization ◽  
Equality Constraints ◽  
Feasible Region ◽  
Mathematical Methods ◽  
Minimization Technique ◽  
Nonlinear Equality

This paper presents a technique for solving nonlinear programming problems with nonconvex feasible regions. The procedure expands the feasible region by replacing nonlinear equality constraints by appropriate inequality constraints. The expansion is used to solve two structural optimization problems using the sequential unconstrained-minimization technique of Fiacco and McCormick. The solutions are compared with solutions obtained by classical mathematical methods.

Indirect Optimization for Finite-Thrust Orbital Interception Problem

2013 ◽  
Vol 313-314 ◽  
pp. 1051-1054
Author(s):  
Yan Yi Huang ◽  
Guo Dong Chen
Keyword(s):  
Nonlinear Programming ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Time History ◽  
Minimum Time ◽  
Programming Method ◽  
The Earth ◽  
Finite Thrust ◽  
Nonlinear Programming Method ◽  
Maximum Thrust

The nonlinear programming method is used to study the finite-thrust minimum-time orbital interception problem. Considering the spacecraft with fixed impulse, the Modified Equinoctial Elements are used to describe the movement of the spacecraft in the attached coordinate, and the model of the orbital interception problem is established. Then the trajectory optimization problem is solved by the nonlinear programming method. The simulations demonstrate that the minimum time orbital interception mission is well accomplished, and the spacecraft fly around the earth with maximum thrust magnitude at whole time history.

Optimum Design of Axial Flow Gas Turbine Stage—Part I: Formulation and Analysis of Optimization Problem

1980 ◽  
Vol 102 (4) ◽  
pp. 782-789 ◽  
Author(s):  
S. S. Rao ◽  
R. S. Gupta
Keyword(s):  
Gas Turbines ◽  
Optimization Problem ◽  
Interpolation Method ◽  
Axial Flow ◽  
Unconstrained Minimization ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Variable Metric ◽  
Minimization Technique

The problem of stage design of axial flow gas turbines has been formulated as a nonlinear mathematical programming problem with the objective of minimizing aerodynamic losses and mass of the stage. The aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented in Part I of this paper. The optimization problem is solved by using the interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique with cubic interpolation method of one-dimensional minimization is employed. Problems involving the optimization of efficiency and/or mass of the stage have been solved numerically in Part II of the paper. The results of a sensitivity analysis conducted about the optimum point have also been reported.

Rolling direction prediction of tensegrity robot on the slope based on FEM and GA

2020 ◽  
Vol 234 (19) ◽  
pp. 3846-3858
Author(s):  
Kaikai Zhao ◽  
Jian Chang ◽  
Bin Li ◽  
Wenjuan Du
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Finite Element ◽  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Rolling Direction ◽  
Unconstrained Minimization ◽  
Unconstrained Optimization Problem ◽  
Minimization Technique ◽  
Element Method

Six-strut tensegrity robot is a new mobile robot whose outer surface is an icosahedron containing 8 regular triangles and 12 isosceles triangles, and the robot performs rolling locomotion along the edges of the triangle. On the slope, it has lots of poses depending on the slope’s angles and positions of robot, which is difficult to control the rolling directions in the real world. This paper proposed a new method based on finite element method and a genetic algorithm to predict the rolling directions of the robot. The balanced forces equations of robot nodes are established using finite element method, which is a constrained optimization problem. The equations are transformed into an unconstrained optimization problem by the thinking of sequential unconstrained minimization technique. Finally, the unconstrained optimization problem is calculated by genetic algorithm, and the relations between the actuators and the rolling directions are obtained through the dot product of gravitational torque and the edge vector of bottom triangle. This method is verified by simulation and experiment results.

Optimum Design of Axial Flow Gas Turbine Stage—Part II: Solution of the Optimization Problem and Numerical Results

1980 ◽  
Vol 102 (4) ◽  
pp. 790-797 ◽  
Author(s):  
S. S. Rao ◽  
R. S. Gupta
Keyword(s):  
Gas Turbines ◽  
Optimization Problem ◽  
Interpolation Method ◽  
Axial Flow ◽  
Unconstrained Minimization ◽  
Problem Formulation ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Variable Metric ◽  
Minimization Technique

The problem of stage design of axial flow gas turbines has been formulated as a nonlinear mathematical programming problem with the objective of minimizing aerodynamic losses and mass of the stage. The aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented in Part I of this paper. The optimization problem is solved by using the interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique with cubic interpolation method of one dimensional minimization is employed. Problems involving the optimization of efficiency and/or mass of the stage have been solved numerically in Part II of the paper. The results of sensitivity analysis conducted about the optimum point have also been reported.

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