5 research outputs found
A note on the paper Fractional Programming with convex quadratic forms and functions by H.P.Benson
In this technical note we give a short proof based on standard results in convex analysis of
some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is
slightly general since we do not specify the convex set X. For clarity we use the same notation
for the different equivalent optimization problems as done in [1]
Optimising portfolio diversification and dimensionality
A new framework for portfolio diversification is introduced which goes beyond
the classical mean-variance approach and portfolio allocation strategies such
as risk parity. It is based on a novel concept called portfolio dimensionality
that connects diversification to the non-Gaussianity of portfolio returns and
can typically be defined in terms of the ratio of risk measures which are
homogenous functions of equal degree. The latter arises naturally due to our
requirement that diversification measures should be leverage invariant. We
introduce this new framework and argue the benefits relative to existing
measures of diversification in the literature, before addressing the question
of optimizing diversification or, equivalently, dimensionality. Maximising
portfolio dimensionality leads to highly non-trivial optimization problems with
objective functions which are typically non-convex and potentially have
multiple local optima. Two complementary global optimization algorithms are
thus presented. For problems of moderate size and more akin to asset allocation
problems, a deterministic Branch and Bound algorithm is developed, whereas for
problems of larger size a stochastic global optimization algorithm based on
Gradient Langevin Dynamics is given. We demonstrate analytically and through
numerical experiments that the framework reflects the desired properties often
discussed in the literature
Modeling Industrial Lot Sizing Problems: A Review
In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research