Showing papers on "Continuous optimization published in 1985"

Structural optimization by multilevel decomposition

Abstract: A method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described The decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem Each element optimization and optimum sensitivity analysis yields the cross-sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness The assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses The method is introduced as a special case of a multilevel, multidisciplinary system optimization and its algorithm is fully described for two-level optimization for structures assembled of finite elements of arbitrary type Numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem

Optimization Modeling of Water Quality in an Uncertain Environment

Abstract: An optimization model with an ability to reflect uncertainties present in water quality problems is described. The technique employed is chance constrained programming wherein probabilistic constraints in a water quality optimization problem are replaced with their deterministic equivalents. The uncertainty inherent in the random elements of the problem is characterized using first-order uncertainty analysis for the case study described.

Algorithm Models for Nondifferentiable Optimization

Abstract: It is shown that a number of seemingly unrelated nondiflerentiable optimization algorithms are special cases of two simple algorithm models: one for constrained and one for unconstrained optimization. In both of these models, the direction finding procedures use parametrized families of maps which are locally uniformly u.s.c. with respect to the generalized gradients of the functions defining the problem. The selection of the parameter is determined by a rule which is analogous to the one used in methods of feasible directions.

Extending monotone and non-expansive mappings by optimization.

Abstract: A theoretical application of optimization theory is demonstrated. The theory is used to prove theorems on the extendeability of the domain of non-expansive, and (strictly) monotone, mappings (under preservation of the characteristic property), by formulating the key problem in it as an optimization problem.

A modified Bernstein-technique for estimating noise-perturbed function values

Abstract: A Bernstein-type improvement of the Bienayme-Chebyshev inequality is presented for evaluating a general class of noise-perturbed functions. This result can be applied in the course of solving stochastic optimization problems.