Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsification

The Markowitz mean-variance portfolio optimization model aims to balance expected return and risk when investing. However, there is a significant limitation when solving large portfolio optimization problems efficiently: the large and dense covariance matrix. Since portfolio performance can be potentially improved by considering a wider range of investments, it is imperative to be able to solve large portfolio optimization problems efficiently, typically in microseconds. We propose dimension reduction and increased sparsity as remedies for the covariance matrix. The size reduction is based on predictions from machine learning techniques and the solution to a linear programming problem. We find that using the efficient frontier from the linear formulation is much better at predicting the assets on the Markowitz efficient frontier, compared to the predictions from neural networks. Reducing the covariance matrix based on these predictions decreases both runtime and total iterations. We also present a technique to sparsify the covariance matrix such that it preserves positive semi-definiteness, which improves runtime per iteration. The methods we discuss all achieved similar portfolio expected risk and return as we would obtain from a full dense covariance matrix but with improved optimizer performance.Comment: 14 pages, 3 figure

Optimal land conservation decisions for multiple species

Given an allotment of land divided into parcels, government decision-makers, private developers, and conservation biologists can collaborate to select which parcels to protect, in order to accomplish sustainable ecological goals with various constraints. In this paper, we propose a mixed-integer optimization model that considers the presence of multiple species on these parcels, subject to predator-prey relationships and crowding effects.Comment: 10 pages, 4 figures. Proceedings of the 52nd Northeast Decision Sciences Institute (NEDSI) Annual Conference, Washington, D

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software.Comment: 8 pages, 2 figure

Microdeletion syndromes, balanced translocations, and gene mapping.

High resolution prometaphase chromosome banding has allowed the detection of discrete chromosome aberrations which escaped earlier metaphase examinations. Consistent tiny deletions have been detected in some well established malformation syndromes: an interstitial deletion in 15q11/12 in the majority of patients with the Prader-Willi syndrome and in a minority of patients with the Angelman (happy puppet) syndrome; a terminal deletion of 17p13.3 in most patients examined with the Miller-Dieker syndrome; an interstitial deletion of 8q23.3/24.1 in a large majority of patients with the Giedion-Langer syndrome; an interstitial deletion of 11p13 in virtually all patients with the WAGR (Wilms' tumour-aniridia-gonadoblastoma-retardation) syndrome; and an interstitial deletion in 22q11 in about one third of patients with the DiGeorge sequence. In addition, a combination of chromosome prometaphase banding and DNA marker studies has allowed the localisation of the genes for retinoblastoma and for Wilms' tumour and the clarification of both the autosomal recessive nature of the mutation and the possible somatic mutations by which the normal allele can be lost in retina and kidney cells. After a number of X linked genes had been mapped, discrete deletions in the X chromosome were detected by prometaphase banding with specific attention paid to the sites of the gene(s) in males who had from one to up to four different X linked disorders plus mental retardation. Furthermore, the detection of balanced translocations in probands with disorders caused by autosomal dominant or X linked genes has allowed a better insight into the localisation of these genes. In some females with X linked disorders, balanced X; autosomal translocations have allowed the localisation of X linked genes at the breakpoint on the X chromosome. Balanced autosome; autosome translocations segregating with autosomal dominant conditions have provided some clues to the gene location of these conditions. In two conditions, Greig cephalopolysyndactyly and dominant aniridia, two translocation families with one common breakpoint have allowed quite a confident location of the genes at the common breakpoint at 7p13 and 11p13, respectively