DRIP Numerical Optimizer

As of 2.63 Drip is being transitioned. Please email [email protected] for any other details while in transition.

v2.63 1 March 2017

DRIP Numerical Optimizer is a collection of Java libraries for Numerical Optimization and Spline Functionality.

DRIP Numerical Optimizer is composed of the following main libraries:

• Numerical Optimization Library
• Spline Model Library

For Installation, Documentation and Samples, and the associated supporting Numerical Libraries please check out [DRIP] (https://github.com/lakshmiDRIP/DRIP).

##Features

###Numerical Optimization ####Fixed Point Finder

• Framework
• Search Initialization
• Bracketing
• Objective Function Failure
• Bracketing Start Initialization
• Open Search Initialization
• Search/Bracketing Initializer Heuristic Customization
• Numerical Challenges in Search
• Variate Iteration
• Open Search Method - Newton's Method
• Closed Search Methods - Secant
• Closed Search Methods - Bracketing Iterative Search
• Closed Search Methods - Univariate Iterator Primitive: Bisection
• Closed Search Methods - Univariate Iterator Primitive: False Position
• Closed Search Methods - Univariate Iterator Primitive: Inverse Quadratic
• Closed Search Methods - Univariate Iterator Primitive: Ridder's
• Closed Search Methods - Univariate Iterator Primitive: Brent and Zheng
• Polynomial Root Search

####Meta-heuristics

• Properties and Classification
• Techniques
• Meta-heuristic Techniques in Combinatorial Problems

####Convex Optimization - Problem Space Specification

• Convex Sets and Convex Hull
• Properties of Convex Sets/Functions
• Convex Optimzation Problems

####Numerical Optimization - Approaches and Solutions

• Newton's Method in Optimization
• Higher Dimensions
• Wolf Conditions
• Armijo Rule and Curvature Condition
• Rationale for the Wolfe Conditions

####Constrained Optimization

• Definition and Description
• General Form
• Solution Methods
• Constraint Optimization: Branch and Bound
• Branch-and-Bound: First Choice Bounding Conditions
• Branch and Bound: Russian Doll Search
• Branch and Bound: Bucket Elimination

####Lagrange Multipliers

• Problem Formulation
• Handling Multiple Constraints
• Formulation via Differentiable Manifolds
• Interpretation of the Lagrange Multipliers
• Sample: Maximal Information Entropy
• Sample: Numerical Optimization Techniques

####Karush-Kuhn-Tucker Conditions

• Necessary Conditions for Optimization Problems
• Regularity Conditions or Constraint Qualifications
• Sufficient Conditions
• KKT Conditions Example - Economics
• KKT Conditions Example - Value Function
• KKT Generalizations

####Interior Point Method

• Interior Point Methodology and Algorithm

###Spline Builder ####Calibration Framework

####Spline Builder Setup

• Design Objective Behind Interpolating Splines
• Base Formulation

####B-Splines

• B-Spline Derivatives

####Polynomial Spline Basis Function

• Polynomial SPline Basis Functions
• Bernstein Polynomial Basis Functions

####Local Spline Stretches

• Local Interpolating/Smoothing Spline Stretches
• Space Curves and Loops

####Spline Segment Calibration

• Smoothing Best Fit Splines
• Segment Best Fit Response with Constraint Matching

####Spline Jacobian

• Optimizing Spline Basis Function Jacobian
• Spline Input Quote Sensitivity Jacobian

####Shape Preserving Spline

• Shape Preserving Tension Spline
• Shape Preserving Nu Splines
• Alternate Tension Spline Formulations

####Koch-Lyche-Kvasov Tension Splines

####Smoothing Splines

• Penalty Minimization Risk Function
• Smoothing Spline Setup
• Ensemble Averaging vs. Basis Spline Representation
• Least Squares Exact Fit + Curvature + Segment Length Penalty Formulation
• Alternate Smootheners

####Multi-dimensional Splines

##Contact

[email protected]