Solution of and bounding in a linearly constrained optimization problem with convex, polyhedral objective function

1995 ◽  
Vol 70 (1-3) ◽  
pp. 1-16 ◽  
Author(s):  
András Prékopa ◽  
Wenzhong Li
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Linearly Constrained Optimization ◽  
Convex Polyhedral ◽  
Linearly Constrained

Teeth-Number Synthesis of an Automatic Planetary Transmission Using Evolutionary Computation

2004 ◽  
Author(s):  
P. A. Simionescu ◽  
D. G. Beale ◽  
G. V. Dozier
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Evolutionary Computation ◽  
Optimization Problem ◽  
Design Parameters ◽  
Constrained Optimization Problem ◽  
Gear Teeth ◽  
Estimation Of Distribution ◽  
Number Synthesis ◽  
Planetary Transmission

The gear-teeth number synthesis of an automatic planetary transmission used in automobiles is formulated as a constrained optimization problem that is solved with the aid of an Estimation of Distribution Algorithm. The design parameters are the teeth number of each gear, the number of multiple planets and gear module, while the objective function is defined based on the departure between the imposed and the actual gear ratios, constrained by teeth-undercut avoidance, limiting the maximum overall diameter of the transmission and ensuring proper planet spacing.

A Computer-Aided Optimization Approach for the Design of Injection Mold Cooling Systems

1998 ◽  
Vol 120 (2) ◽  
pp. 165-174 ◽  
Author(s):  
L. Q. Tang ◽  
K. Pochiraju ◽  
C. Chassapis ◽  
S. Manoochehri
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Constrained Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Temperature Gradients ◽  
Optimization Approach ◽  
Injection Mold ◽  
Constrained Optimization Problem ◽  
Cooling Systems

A methodology is presented for the design of optimal cooling systems for injection mold tooling which models the mold cooling as a nonlinear constrained optimization problem. The design constraints and objective function are evaluated using Finite Element Analysis (FEA). The objective function for the constrained optimization problem is stated as minimization of both a function related to part average temperature and temperature gradients throughout the polymeric part. The goal of this minimization problem is to achieve reduction of undesired defects as sink marks, differential shrinkage, thermal residual stress built-up, and part warpage primarily due to non-uniform temperature distribution in the part. The cooling channel size, locations, and coolant flow rate are chosen as the design variables. The constrained optimal design problem is solved using Powell’s conjugate direction method using penalty function. The cooling cycle time and temperature gradients are evaluated using transient heat conduction simulation. A matrix-free algorithm of the Galerkin Finite Element Method (FEM) with the Jacobi Conjugate Gradient (JCG) scheme is utilized to perform the cooling simulation. The optimal design methodology is illustrated using a case study.

Error Compensation Based on Lagrange Multiplier in Heterodyne Laser Interferometer

2014 ◽  
Vol 681 ◽  
pp. 43-46
Author(s):  
Eun Hwan Oh ◽  
Woo Ram Lee ◽  
Kyung Hyun Lee ◽  
Kwan Ho You
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Lagrange Multiplier ◽  
Error Compensation ◽  
Optimization Problem ◽  
Laser Interferometer ◽  
Length Measurement ◽  
Constrained Optimization Problem ◽  
Compensation Algorithm ◽  
Heterodyne Laser Interferometer

In this paper, we propose a signal compensation algorithm. In heterodyne laser interferometer, the unexpected error restricts the precision such as nonlinearity and environmental error. To improve the accuracy in length measurement, we use the method of Lagrange multiplier which solves the constrained optimization problem and allows to minimize an objective function. With the method of Lagrange, we apply it to a length measurement and show the result of simulation.

A Constrained Optimization Technique to Improve the Performance of Strain Gauge Transducers

1986 ◽  
Vol 200 (2) ◽  
pp. 135-141 ◽  
Author(s):  
B L MacCarthy ◽  
J M Sharp ◽  
N D Burns
Keyword(s):  
Constrained Optimization ◽  
Strain Gauge ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Optimization Strategy ◽  
Constrained Optimization Problem ◽  
Design Problems ◽  
Wide Range ◽  
Linearly Constrained ◽  
Output Characteristics

An optimization strategy is developed to improve the performance of strain gauge transducers. For a specific transducer configuration, the method used is to select an output characteristic to be optimized and to set realistic constraints on the remaining output characteristics and on physical dimensions. Using this strategy, a non-linearly constrained optimization problem may be formulated mathematically. Numerical methods to solve problems of this type are discussed and practical details arising from their use are considered. Correctly formulated problems are solvable quickly and efficiently with routines which are generally available. The techniques introduced here are applicable to a wide range of design problems in transducers of this type and provide a significant design aid.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

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