Nonlinear Optimization 1981

Nonlinear Optimization

Given a single function f that depends on one or more independent variable, we want to find the values of those variables where f is maximized or minimized. Often the computational cost is dominated by the the cost of evaluating f (and also perhaps its partial derivatives with respect to all variables). Finding a global extremum is, in general, a very difficult problem. Two standard heuristics ...

Nonlinear Optimization

The nonlinear minimization problem is to find a (local) minimizer for an objective function f (·), which takes in a vector x ∈ R n as input and a scalar f (x) as output. A broad and important class of algorithms take an iterative form x k+1 = x k + α k h where if f x k = 0, we choose direction h k so that f x k h k < 0 and the step size α k so that f x k + α k h k < f x k. At current ponit x, c...

OPTIMIZATION FORMULATION FOR NONLINEAR STRUCTURAL ANALYSIS

In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path&rsquo;s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was p...

Applied nonlinear optimization

Modelling and simulation of complex processes in key technologies are the main issues of the DFG research center. Being able to efficiently deal with the complex models established and having the corresponding mathematical basis available, engineers and practitioners are interested in optimizing these models according to some objective. This is reflected by several scientific projects in the ce...

Introduction to Nonlinear Optimization