 # Optimization

Field Guide to ILP Solvers in R for Conservation Prioritization. In this post I’ll compare alternative integer linear programming (ILP) solvers for conservation planning. The goal is to develop a tool to solve the Marxan reserve design problem using ILP rather than simulated annealing. Unlike simulated annealing, ILP can find the true global optimum of an optimization problem or, if time constraints are an issue, it can return a solution that is within a specified distance form the optimum.

This ability to evaluate the quality of a solution, makes IP an excellent candidate for conservation planning. In a previous post, I demonstrated how to use the commercial optimization software Gurobi. Gurobi is great, but expensive, so in this post I’ll explore solving the reserve design problem using free and open-source solvers. In general, the goal of an optimization problem is to minimize an objective function over a set of decision variables, subject to a series of constraints. Mixed Integer Programming in R with the ompr package. Choosing which method to use for “optimizing” functions – Blog: John C. Nash.

A decision tree for function minimization What R calls “optimization” is more generally known as function minimization. The tools in the stats package function optim() are all essentially function mimizers, as are those in the package optimrx found at optimrx tries to make it easier for users to call quite a few methods without having to learn many different sets of command syntax. It uses the same syntax as optim(), even down to parameter scaling, by changing the method=”name” argument. There are, however, a number of methods. Which is best for your purpose? Portfolio Optimization using R and Plotly. In this post we’ll focus on showcasing Plotly’s WebGL capabilities by charting financial portfolios using an R package called PortfolioAnalytics. The package is a generic portfolo optimization framework developed by folks at the University of Washington and Brian Peterson (of the PerformanceAnalytics fame). You can see the vignette here Let’s pull in some data first. library(PortfolioAnalytics) library(quantmod) library(PerformanceAnalytics) library(zoo) library(plotly) # Get data getSymbols(c("MSFT", "SBUX", "IBM", "AAPL", "^GSPC", "AMZN")) # Assign to dataframe # Get adjusted prices prices.data <- merge.zoo(MSFT[,6], SBUX[,6], IBM[,6], AAPL[,6], GSPC[,6], AMZN[,6]) # Calculate returns returns.data <- CalculateReturns(prices.data) returns.data <- na.omit(returns.data) # Set names colnames(returns.data) <- c("MSFT", "SBUX", "IBM", "AAPL", "^GSPC", "AMZN") # Save mean return vector and sample covariance matrix meanReturns <- colMeans(returns.data) covMat <- cov(returns.data)

Quantitate: More on Quadratic Progamming in R. Journal of Statistical Software — Show. Vincent Zoonekynd's Blog. Fri, 01 Jun 2012: Optimization Many problems in statistics or machine learning are of the form "find the values of the parameters that minimize some measure of error". But in some cases, constraints are also imposed on the parameters: for instance, that they should sum up to 1, or that at most 10 of them should be non-zero -- this adds a combinatorial layer to the problem, which makes it much harder to solve. In this note, I will give a guide to (some of) the optimization packages in R and explain (some of) the algorithms behind them. The solvers accessible from R have some limitations, such as the inability to deal with binary or integral constraints (in non-linear problems): we will see how to solve such problems. When you start to use optimization software, you struggle to coax the problem into the form expected by the software (you often have to reformulate it to make it linear or quadratic, and then write it in matrix form).

Introduction Local extrema Find x1,... The problem becomes. Optimization in R (Part I) This post is the first in a series on solving practical convex optimization problems with R. My goal for the series is to work up to some interesting applications of the constrained optimization libraries available in R. In particular, I plan to work out some test cases and practical examples using the quadprog package. Notes on Optimization with R. Vincent Zoonekynd's Blog. Solving Quadratic Progams with R's quadprog package. In this post, we'll explore a special type of nonlinear constrained optimization problems called quadratic programs. Quadratic programs appear in many practical applications, including portfolio optimization and in solving support vector machine (SVM) classification problems. There are several packages available to solve quadratic programs in R. Here, we'll work with the quadprog package. Before we dive into some examples with quadprog, we'll give a brief overview of the terminology and mechanics of quadratic programs. Quick Overview of Quadratic Programming In a quadratic programming problem, we consider a quadratic objective function: Q(x) = \frac{1}{2} x^T D x - d^T x + c. Here, x is a vector in \mathbb{R}^n, D is an n \times nsymmetric positive definite matrix, d is a constant vector in \mathbb{R}^n and c is a scalar constant. We also impose a system of linear constraints on the vector x \in \mathbb{R}^n.

Example #1: Example #2: Let's inspect the optimal allocation: The Circus Tent Problem with R's Quadprog. The MathWorks has an interesting demo on how the shape of a circus tent can be modeled as the solution of a quadratic program in MATLAB. In this post, we'll show how to solve this same problem in R using the quadprog package and also provide the technical details not covered in the Mathwork's example. In particular, we'll explain how an energy function is associated to this problem and how descretizing this energy function gives rise to a sparse quadratic program. Quadratic programming is a powerful and versatile technique that has found applications in a diverse range of fields. Perhaps its most famous application is in portfolio allocation theory, though it also is very well known as the computational foundation of SVM.