22 research outputs found
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
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
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
Global convergence of a primal-dual interior-point method for nonlinear programming
Many recent convergence results obtained for primal-dual interior-point methods for nonlinear programming, use assumptions of the boundedness of generated iterates. In this paper we replace such assumptions by new assumptions on the NLP problem, develop a modification of a primal-dual interior-point method implemented in software package LOQO and analyze convergence of the new method from any initial guess
Interior-point methods for nonconvex nonlinear programming: filter-methods and merit functions.
Abstract. In this paper, we present a barrier method for solving nonlinear programming problems. It employs a Levenberg-Marquardt perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We show that the Levenberg-Marquardt perturbation is equivalent to replacing the Newton step by a cubic regularization step with an appropriately chosen regularization parameter. This equivalence allows us to use the favorable theoretical results o
Interior-point methods for nonconvex nonlinear programming: Orderings and higher-order methods
Abstract. In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the loqo algorithm and provide extensive numerical results on the CUTEr test set and on warmstarting in the context of quadratic, nonlinear, mixed integer nonlinear, and goal programming. 1