Single Variable Unconstrained Optimization Techniques Using Interval Analysis

Interval Analysis: Unconstrained and Constrained Optimization

INTERVAL ANALYSIS: UNCON-STRAINED AND CONSTRAINED OPTIMIZATION Introduction. Interval algorithms for constrained and un-constrained optimization are based on adaptive, exhaustive search of the domain. Their overall structure is virtually identical to Lipschitz optimization as in [4], since interval evaluations of an objective function φ over an interval vector x correspond to estimation of the ...

Recursive subspace identification based on instrumental variable unconstrained quadratic optimization

The problem of the recursive formulation of the MOESP class of subspace identification algorithms is considered and two novel instrumental variable approaches are introduced. The first one leads to an RLS-like implementation, the second to a gradient type iteration. The relative merits of both approaches are analysed and discussed, while simulation results are used to compare their performance ...

Line search methods with variable sample size for unconstrained optimization

Minimization of unconstrained objective function in the form of mathematical expectation is considered. Sample Average Approximation SAA method transforms the expectation objective function into a real-valued deterministic function using large sample and thus deals with deterministic function minimization. The main drawback of this approach is its cost. A large sample of the random variable tha...

Using unconstrained elite archives for multiobjective optimization

Deterministic global optimization of molecular structures using interval analysis

The search for the global minimum of a molecular potential energy surface is a challenging problem. The molecular structure corresponding to the global minimum is of particular importance because it usually dictates both the physical and chemical properties of the molecule. The existence of an extremely large number of local minima, the number of which may increase exponentially with the size o...