It is demonstrated that substantial savings in the computer storage space and calculation can be effected by a close inspection of the subsearch phase of a multivariate optimization algorithm. This is particularly imp...
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It is demonstrated that substantial savings in the computer storage space and calculation can be effected by a close inspection of the subsearch phase of a multivariate optimization algorithm. This is particularly important in implementing algorithms on small computers. A significant compaction of the golden section search is developed. Coincidentally, it is found that the actual bracketing and convergence properties are better than those conventionally used in the literature.
作者：
SOHONI, VHAUG, EJV. Sohoni
E. J. Haug Materials Division College of Engineering The University of Iowa Iowa City Iowa 52242
Problems of optimal kinematic synthesis of mechanisms and machines are formulated in a state space setting that allows for treatment of large scale systems with general design objectives and constraints. An iterative ...
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Problems of optimal kinematic synthesis of mechanisms and machines are formulated in a state space setting that allows for treatment of large scale systems with general design objectives and constraints. An iterative kinematic analysis method is presented. An adjoint variable method of design sensitivity analysis is presented that uses the same matrices generated in kinematic analysis to efficiently calculate derivatives of cost and constraint functions with respect to design. A gradient projection optimization algorithm is presented, based on the state space kinematic and design sensitivity analysis formulation. Two mechanism synthesis problems are solved to illustrate the method and to evaluate its effectiveness.
作者：
SOHONI, VNHAUG, EJV. N. Sohoni
E. J. Haug Division of Materials Engineering College of Engineering The University of Iowa Iowa City Iowa 52242
Problems of optimal design of mechanisms are formulated in a state space setting that allows treatment of general design objectives and constraints. A constrained multi-element technique is employed for velocity, acce...
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Problems of optimal design of mechanisms are formulated in a state space setting that allows treatment of general design objectives and constraints. A constrained multi-element technique is employed for velocity, acceleration, and kineto-static analysis of mechanisms. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions involving kinematic, force, and design variables. A generalized steepest descent optimization algorithm is employed, using the design sensitivity analysis methods developed, as the basis for a general purpose kinematic system optimization algorithm. Two optimal design problems are solved to demonstrate effectiveness of the method.
Two recent methods (Shanno, 1978; Toint, 1980) for revising estimates of sparse second derivative matrices in quasi-Newton optimization algorithms reduce to variable metric formulae when there are no sparsity conditio...
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Two recent methods (Shanno, 1978; Toint, 1980) for revising estimates of sparse second derivative matrices in quasi-Newton optimization algorithms reduce to variable metric formulae when there are no sparsity conditions. It is proved that these methods are equivalent. Further, some examples are given to show that the procedure may make the second derivative approximations worse when the objective function is quadratic. Therefore the convergence properties of the procedure are sometimes less good than the convergence properties of other published methods for revising sparse second derivative approximations.
The auxiliary problem principle allows one to find the solution of a problem (minimization problem, saddle-point problem, etc.) by solving a sequence of auxiliary problems. There is a wide range of possible choices fo...
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The auxiliary problem principle allows one to find the solution of a problem (minimization problem, saddle-point problem, etc.) by solving a sequence of auxiliary problems. There is a wide range of possible choices for these problems, so that one can give special features to them in order to make them easier to solve. We introduced this principle in Ref. 1 and showed its relevance to decomposing a problem into subproblems and to coordinating the subproblems. Here, we derive several basic or abstract algorithms, already given in Ref. 1, and we study their convergence properties in the framework of i infinite-dimensional convex programming.
The concept of a hierarchy of performance models is introduced. It is argued that such a hierarchy should consist of models spanning a wide range of accuracy and cost in order to be a cost-effective tool in the design...
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The concept of a hierarchy of performance models is introduced. It is argued that such a hierarchy should consist of models spanning a wide range of accuracy and cost in order to be a cost-effective tool in the design of computer systems. Judicious use of the hierarchy can satisfy the conflicting needs of high accuracy and low cost of performance evaluation. A system design procedure that uses the hierarchy is developed. The concepts developed are illustrated by applying them to a case study of system design. The results of optimizations conducted using a two-level performance model hierarchy and a simple cost model are discussed. In almost all the experiments conducted, the optimization procedure converged to a region very close to a locally optimum system. The efficiency of the procedure is shown to be considerably greater than that of the brute force approach to system design. [ABSTRACT FROM AUTHOR]
Abstract: In this paper we suggest a single bench mark problem family for use in evaluating unconstrained minimization algorithms or routines. In essence, this problem consists of measuring, for each algorithm...
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Abstract: In this paper we suggest a single bench mark problem family for use in evaluating unconstrained minimization algorithms or routines. In essence, this problem consists of measuring, for each algorithm, the rate at which it descends an unlimited helical valley. The periodic nature of the problem allows us to exploit affine scale invariance properties of the algorithm. As a result, the capacity of the algorithm to minimize a wide range of helical valleys of various scales may be summarized by calculating a single valued function ${g_Q}({X_1})$. The measurement of this function is not difficult, and the result provides information of a simple, general character for use in decisions about choice of algorithm.
Abstract: Let $f(x)$ be a general objective function and let $\bar f(x) = h + mf(Ax + d)$. An analytic estimation of the minimum of one would resemble an analytic estimation of the other in all nontrivial resp...
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Abstract: Let $f(x)$ be a general objective function and let $\bar f(x) = h + mf(Ax + d)$. An analytic estimation of the minimum of one would resemble an analytic estimation of the other in all nontrivial respects. However, the use of a minimization algorithm on either might or might not lead to apparently unrelated sequences of calculations. This paper is devoted to providing a general theory for the affine scale invariance of algorithms. Key elements in this theory are groups of transformations T whose elements relate $\bar f(x)$ and $f(x)$ given above. The statement that a specified algorithm is scale invariant with respect to a specified group T is defined. The scale invariance properties of several well-known algorithms are discussed.
A constrained optimization algorithm to maximize the operating speed of a fifteen degree-of-freedom lateral dynamic model for a passenger railcar subject to random alignment irregularities is presented in this paper. ...
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A constrained optimization algorithm to maximize the operating speed of a fifteen degree-of-freedom lateral dynamic model for a passenger railcar subject to random alignment irregularities is presented in this paper. The constraints placed on the optimization problem limit the passenger discomfort, primary and secondary suspension clearance, the wheel slippage, and secondary suspension stroke to practical values while traversing a curve. The optimization results demonstrate that the primary suspension system and the wheel conicity have the most profound influence on maximizing the critical speed where “hunting” begins. The maximum critical speed is insensitive to large variations in secondary yaw stiffness. The secondary lateral stiffness has less effect on the maximum critical speed than the primary lateral stiffness. Thus, the secondary stiffness can be chosen primarily to satisfy passenger ride comfort specifications. The maximum critical speed is quite sensitive to whether the wheel is new, slightly worn, or severely worn.
A new procedure for numerical optimization of constrained nonlinear problems is described. The method makes use of an efficient “Boundary Tracking” strategy to move on the constraint surfaces. In a comparison study ...
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A new procedure for numerical optimization of constrained nonlinear problems is described. The method makes use of an efficient “Boundary Tracking” strategy to move on the constraint surfaces. In a comparison study it was found to be an effective method for treating nonlinear mathematical programming problems particularly those with difficult nonlinear constraints.
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