Computational Algorithm for the Sequential Unconstrained Minimization Technique for Nonlinear Programming

1964 ◽  
Vol 10 (4) ◽  
pp. 601-617 ◽  
Author(s):  
Anthony V. Fiacco ◽  
Garth P. McCormick
Keyword(s):  
Nonlinear Programming ◽  
Computational Algorithm ◽  
Unconstrained Minimization ◽  
Minimization Technique

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.

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.

Optimal Thermal Design of Fin-and-Tube Heat Exchangers by Integration of a SUMT and a SCGM

2016 ◽  
Author(s):  
Xinyi Li ◽  
Ting Ma ◽  
Qiuwang Wang
Keyword(s):  
Heat Exchangers ◽  
Optimization Technique ◽  
Unconstrained Minimization ◽  
Geometric Parameters ◽  
Thermal Design ◽  
Trial And Error ◽  
Heat Transfer Area ◽  
Compact Heat Exchangers ◽  
Minimization Technique ◽  
Combined Structure

It is a recognized hard task for the traditional thermal design of compact heat exchangers to obtain the optimal geometric parameters efficiently and effectively, owing to its complex trial-and-error process. In response to this issue, a simplified conjugate-gradient method (SCGM) combined with a sequential unconstrained minimization technique (SUMT) as a favorable optimization technique is incorporated with the traditional thermal design in this study, and then the key geometric parameters of fin-and-tube heat exchangers (FTHEs) are investigated and optimized successfully. In this method, the minimum total weight of FTHEs as the final objective is discussed, involving two geometric parameters, diameter of tube and height of shape as search variables. Aiming to minimize the objective function, SCGM is introduced to the SUMT to update the search variables continually with the fixed search steps and the search directions. Meanwhile, with the known geometric parameters from the SUMT, the log-mean temperature difference method (LMTD) is applied to determine the heat transfer area under the combined structure sizes for a given heat duty. Additionally, optimization results for three different heat duty is discussed in this work. The results show that it is effective to obtain the optimal sets of geometric parameters of FTHEs by the present method, and there are some guidance values for the thermal designs of compact heat exchangers.

Reliability Based Optimization of Submarine Pressure Hulls With Inelastic Interstiffener Buckling Failure

2006 ◽  
Author(s):  
P. Radha ◽  
K. Rajagopalan
Keyword(s):  
Unconstrained Minimization ◽  
Computer Code ◽  
Correction Method ◽  
Penalty Function Method ◽  
Simulation Design ◽  
Design Variables ◽  
Minimization Technique ◽  
Buckling Failure ◽  
Optimal Values ◽  
Reliability Based Optimization

Uncertainties that exist in modelling and simulation, design variables and parameters, manufacturing processes etc., may lead to large variations in the performance characteristics of the system. Optimized deterministic designs determined without considering uncertainties can be unreliable and may lead to catastrophic failure of the structure being designed. Reliability based optimization (RBO) is a methodology that addresses these problems. In this paper the reliability based optimization of submarine pressure hulls in which the failure gets governed by inelastic interstiffener buckling has been described. The problem has been formulated to minimize the ratio of weight of shell-stiffener geometry to the weight of liquid displaced, subjected to reliability based inelastic interstiffener buckling constraint. Since the methods of analysis of inelastic buckling failure of submarine pressure hulls are inadequate, in the present study the Johnson-Ostenfeld inelastic correction method has been adopted for formulating the constraint. By considering spacing of the stiffener, thickness of the plating and depth of the stiffener as the design variables, Sequential Unconstrained Minimization Technique (SUMT) has been used to solve the design problem. RBO has been carried out to get the optimal values of these design variables for a target reliability index using Interior Penalty Function Method for which an efficient computer code in C++ has been developed.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

Design of Transverse-Plane Bulkheads in Tankers

1976 ◽  
Vol 20 (02) ◽  
pp. 67-78
Author(s):  
Carl Arne Carlsen ◽  
Dag Kavlie
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Unconstrained Minimization ◽  
Optimization Methods ◽  
Transverse Plane ◽  
Design Stage ◽  
Preliminary Design Stage ◽  
Minimization Technique ◽  
Institute Of Technology ◽  
Aided Design

A program system, INDETS, for computer-aided design of tanker structures has been developed. The system, which is the result of a joint effort of the Norwegian Institute of Technology, Trondheim, and the Aker Group, Oslo, is considered an effective tool for practical design. A design module of INDETS for tanker transverse-plane bulkheads is presented. The girder system is analyzed by a three-dimensional frame model including the surrounding structure as substructures. Two optimization methods, the Stress Ratio Technique and the Sequential Unconstrained Minimization Technique, are applied. A number of parametric variations on topology have been performed, and the depth and breadth have been varied to derive curves for estimating the weight of bulkheads at the preliminary design stage. As a conclusion, a simple-formula is presented.

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