Constrained and composite optimization via adaptive sampling methods

Some composite-step constrained optimization methods interpreted via the perturbed sequential quadratic programming framework

We consider the inexact restoration and the composite-step sequential quadratic programming (SQP) methods, and relate them to the so-called perturbed SQP framework. In particular, iterations of the methods in question are interpreted as certain structured perturbations of the basic SQP iterations. This gives a different insight into local behaviour of those algorithms, as well as improved or di...

Constrained Inverse Adaptive Cluster Sampling

In adaptive cluster sampling, first proposed by Thompson (1990, 1992) and studied in detail by Thompson and Seber (1996), an initial sample of units is selected and, whenever the value of the variable of interest satisfies a specified condition, neighbouring units are added to the sample. The neighbourhood of a unit may be defined by spatial proximity or, in the case of human population, by soc...

Part I: Methods Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set

We present a unified approach to a class of nonconvex global optimization problems with composite monotonic constraints. (By composite monotonic function is meant a function which is the composition of a monotonic function on R n with a mapping from R n → R m with m ≤ n.) This class includes problems with constraints involving products of linear functions, sums of ratio functions, etc., and als...

Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems

Adaptive Augmented Lagrangian Methods for Large-Scale Equality Constrained Optimization

We propose an augmented Lagrangian algorithm for solving large-scale equality constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the cor...