This paper describes SCPIP, a FORTRAN77 subroutine that has been proven to be a reliable implementation of convexprogramming methods in an industrial environment. convex approximation methods like the method of movin...
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This paper describes SCPIP, a FORTRAN77 subroutine that has been proven to be a reliable implementation of convexprogramming methods in an industrial environment. convex approximation methods like the method of moving asymptotes are used nowadays in many software packages for structural optimization. They are known to be efficient tools for the solution of design problems, in particular if displacement dependent constraints like stresses occur. A major advantage over many but not all classical approaches of mathematical programming is that at an iteration point a local model is formulated. For the solution of such a model no further function and gradient evaluations are necessary besides those at the current iteration point. The first versions of convex approximation methods used all a dual approach to solve the subproblems which is still a very efficient algorithm to solve problems with at most a medium number of constraints. But it is not efficient for problems with many constraints. An alternative is the use of an interior point method for the subproblem solution. This leads to more freedom in the definition of the linear systems where most of the computing time to solve the subproblems is spent. In consequence, large-scale problems can be handled more efficiently.
The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the method...
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The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved.
The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well in the context of structural optimization. The two main reasons are that the appro...
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The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well in the context of structural optimization. The two main reasons are that the approximation scheme used for the objective function and the constraints fits very well to these applications and that at an iteration point a local optimization model is used such that additional expensive function and gradient evaluations of the original problem are avoided. The subproblems that occur in both methods are special nonlinear convex programs and have traditionally been solved using a dual approach. This is now replaced by an interior point approach. The latter one is more suitable for large problems because sparsity properties of the original problem can be preserved and the separability property of the approximation functions is exploited. The effectiveness of the new method is demonstrated by a few examples dealing with problems of structural optimization.
＜正＞In mechanical design problems, the method of moving asymptotes is a popular tool to solve the arising optimization problems. For large problems, however, the method often needs too much storage and computing tim...
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＜正＞In mechanical design problems, the method of moving asymptotes is a popular tool to solve the arising optimization problems. For large problems, however, the method often needs too much storage and computing time in its traditional formulation. Therefore, a new approach to solve the subproblems has been defined which gives the possibility to exploit sparsity in the original problem and does not create dense structure itself. Several subapproaches with different advantages and disadvantages are possible. The decision for the best possibility can be done by the computer. A central point of this paper will be the description of SCPIP, the FORTRAN77 realization of these approaches. Up to now the method has been mainly applied to weight optimization and topology design.
This paper identifies the two most efficient non-linear programming techniques for the solution of optimization problems of plane structural frames under multiple load systems. The problem is one of minimizing the mas...
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