Lecture 07: Quadratic Programming (Optimization)
Meaning for a quadratic program (QP) to be convex, strictly convex, and
First-order optimality conditions associated with solving an equality
How to write them in terms of a KKT
570.496 PART 2: Mathematical Models for Managing Environmental Systems
LECTURE 5: Introduction and Overview
* Mathematical ecologists have been modeling relationships of species within ecosystems
since at least the early 20th Century.
* One of the first m
LECTURE 8: Habitat Selection and Management for a Single Species
* Creating nature reserves is one method of biological conservation. Habitat
management is another, complementary method.
* Typically, the goal of habitat management is to influence the popu
LECTURE 6c: Probabilistic Site Selection Models for Species Richness
* The input data to the RSCP and RMCP models are site presence data for the species
(or other features) that need to be represented in the reserve system.
* To use the RSCP and RMCP mode
LECTURE 6a: A Taxonomic Selection Model for Maximizing Biological Diversity
Biological Taxonomy and Diversity
* In the 1970s and 1980s, biological diversity became viewed by many conservation
practitioners as a key attribute in the protection, conservatio
LECTURE 7a: Spatial Optimization Models for Reserve Design
Spatial Criteria for Reserve Design
Diamonds Reserve Design Guidelines
* In a 1975 paper, scientist Jared Diamond compared nature reserves to islands in the
* Diamond developed several geom
LECTURE 9: Reservoir Planning and Management Models
A reservoir is an impoundment of water. Large reservoirs are
typically created by dams either earthen or concrete and steel built in rivers.
* The water stored in a reservoir can be used for a
LECTURE 6b: Reserve Site Selection Models for Species Richness
* Reserve site selection: Suppose that we have a list of species to protect and a list of
candidate reserve sites (delineated areas of land). Each site contains some of the
species on our list
Lecture 00: Introduction to Nonlinear Optimization II
1. Computing gradients, Jacobians, and Hessians of a given function.
2. Basic analysis: Taylor's expansion, continuity, limits, and sequences.
3. Only minimization. What do we do if we want to maximize