Showing papers on "Continuous optimization published in 1980"

A smoothing-out technique for min—max optimization

Abstract: In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR n . Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.

A new approach to optimization of chemical processes

Abstract: Based on recent work by Powell, a new optimization algorithm is presented. It merges the Newton-Raphson method and quadratic programming. A unique feature is that one does not converge the equality and tight inequality constraints for each step taken by the optimization algorithm. The article show how to perform the necessary calculations efficiently for very large problems which require the use of mass memory. Experience with the algorithm on small problems indicates it converges exceptionally quickly to the optimal answer, often in as few iterations (5 to 15) as are needed to perform a single simulation with no optimization using more conventional approaches.

A New Method for Solving Reliability Optimization Problem

Abstract: A simple and computationally attractive method for solving constrained (which may not be linear) reliability optimization problem, when both improved modules and redundancy are used, is presented. Usually only one initial point is sufficient to be considered. The method applies to both series as well as complex systems and some times gives better solution than Tillman et al. (1977).

Optimization of System Reliability via Redundancy and/or Design Considerations

Abstract: The two traditional methods used in improving the reliability of a multi-stage system are examined The first method is the creation of redundancy in system components, whereas the second method consists of overdesigning the system components An Integrated Reliability Optimization Model that includes both of these two methods for improving the reliability of a system is presented It is shown that under certain assumptions the integrated model reduces to a Redundancy Optimization Model and under certain other assumptions reduces to a Design Optimization Model Several methods that have been previously suggested for obtaining solutions to the Integrated Optimization Model are reviewed and a generalized solution procedure for such a model is presented This solution procedure involves the successive solution of two subproblems a number of times The first subproblem is a design optimization problem that is solved by the Davidon-Fletcher-Powell optimization algorithm The second subproblem is a reliability redundancy optimization problem that is solved with the heuristic approach of Aggarwal, et al

Continuous perturbations of infinite optimization problems

Abstract: In this paper, continuity properties of the extremal value function and the solution function are studied for general optimization problems with perturbations in the objective function and the constraints. A classical stability condition is extended and compared with constraint qualification conditions.