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<!doctype html>
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<title>Drip-numerical-optimizer by lakshmiDRIP</title>
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<h1>Drip-numerical-optimizer</h1>
<p>DRIP Numerical Optimizer</p>
<p class="view"><a href="https://github.com/lakshmiDRIP/DRIP-Numerical-Optimizer">View the Project on GitHub <small>lakshmiDRIP/DRIP-Numerical-Optimizer</small></a></p>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Numerical-Optimizer/zipball/master">Download <strong>ZIP File</strong></a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Numerical-Optimizer/tarball/master">Download <strong>TAR Ball</strong></a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP-Numerical-Optimizer">View On <strong>GitHub</strong></a></li>
</ul>
</header>
<section>
<p align="center"><img src="https://github.com/lakshmiDRIP/DRIP/blob/master/DRIP_Logo.gif?raw=true" width="100"></p>
<p><strong>v2.63</strong> <em>1 March 2017</em></p>
<p>DRIP Numerical Optimizer is a collection of Java libraries for Numerical Optimization and Spline Functionality.</p>
<p>DRIP Numerical Optimizer is composed of the following main libraries:</p>
<ul>
<li>Numerical Optimization Library</li>
<li>Spline Model Library</li>
</ul>
<p>For Installation, Documentation and Samples, and the associated supporting Numerical Libraries please check out <a href="https://github.com/lakshmiDRIP/DRIP">DRIP</a>.</p>
<h2>
<a id="drip-core-technical-specifications" class="anchor" href="#drip-core-technical-specifications" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>DRIP Core Technical Specifications</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/AssetAllocation/AssetAllocation_v2.56.pdf">Asset Allocation Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/FixedIncome/FixedIncomeAnalytics_v2.58.pdf">Fixed Income Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/TransactionCost/TransactionCostAnalytics_v2.57.pdf">Transaction Cost Analytics</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/XVA/XVAAnalytics_v2.62.pdf">XVA Analytics</a></li>
</ul>
<h2>
<a id="drip-supporting-technical-specifications" class="anchor" href="#drip-supporting-technical-specifications" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>DRIP Supporting Technical Specifications</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/SplineBuilder/SplineBuilder_v0.82.pdf">Spline Builder Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/NumericalOptimizer/NumericalOptimization_v2.05.pdf">Numerical Optimization Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/StatisticalLearning/StatisticalLearningLibrary_v0.80.pdf">Statistical Learning Library</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification/MachineLearning/MachineLearningLibrary_v0.92.pdf">Machine Learning Library</a></li>
</ul>
<h2>
<a id="additional-documentation" class="anchor" href="#additional-documentation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Additional Documentation</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP">DRIP GitHub Source</a></li>
<li><a href="https://lakshmidrip.github.io/DRIP/Javadoc/index.html">DRIP API Javadoc</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/ReleaseNotes">DRIP Release Notes</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/DRIPSpecification">DRIP Technical Specifications</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/Docs/External">DRIP External Specifications</a></li>
<li>User guide is a work in progress!</li>
</ul>
<h2>
<a id="samples-core-optimizer---need-much-more" class="anchor" href="#samples-core-optimizer---need-much-more" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Core Optimizer - Need much more!)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/rdtor1">R<sup>d</sup>->R<sup>1</sup> Co-variance Ellipsoid</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/descentverifier">Descent Convergence Verifier</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/optimizer">Constrained Optimization Variants</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/semidefinite">Semi-definite Programming</a></li>
</ul>
<h2>
<a id="samples-numerical-support---need-much-more" class="anchor" href="#samples-numerical-support---need-much-more" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Numerical Support - Need much more!)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/matrix">Linear Algebra/Components</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/measure">Closed Distribution Measure</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/statistics">Empirical Distribution Measure</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/numerical">Search/Quadrature/Fourier</a></li>
</ul>
<h2>
<a id="samples-spline-library---need-much-more" class="anchor" href="#samples-spline-library---need-much-more" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Samples (Spline Library - Need much more!)</h2>
<ul>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/spline">Segments and Splines</a></li>
<li><a href="https://github.com/lakshmiDRIP/DRIP/tree/master/org/drip/sample/stretch">Stretches and Grids</a></li>
</ul>
<h2>
<a id="features" class="anchor" href="#features" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Features</h2>
<h3>
<a id="numerical-optimization" class="anchor" href="#numerical-optimization" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Numerical Optimization</h3>
<h4>
<a id="fixed-point-finder" class="anchor" href="#fixed-point-finder" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Fixed Point Finder</h4>
<ul>
<li>Framework</li>
<li>Search Initialization</li>
<li>Bracketing</li>
<li>Objective Function Failure</li>
<li>Bracketing Start Initialization</li>
<li>Open Search Initialization</li>
<li>Search/Bracketing Initializer Heuristic Customization</li>
<li>Numerical Challenges in Search</li>
<li>Variate Iteration</li>
<li>Open Search Method - Newton's Method</li>
<li>Closed Search Methods - Secant</li>
<li>Closed Search Methods - Bracketing Iterative Search</li>
<li>Closed Search Methods - Univariate Iterator Primitive: Bisection</li>
<li>Closed Search Methods - Univariate Iterator Primitive: False Position</li>
<li>Closed Search Methods - Univariate Iterator Primitive: Inverse Quadratic</li>
<li>Closed Search Methods - Univariate Iterator Primitive: Ridder's</li>
<li>Closed Search Methods - Univariate Iterator Primitive: Brent and Zheng</li>
<li>Polynomial Root Search</li>
</ul>
<h4>
<a id="meta-heuristics" class="anchor" href="#meta-heuristics" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Meta-heuristics</h4>
<ul>
<li>Properties and Classification</li>
<li>Techniques</li>
<li>Meta-heuristic Techniques in Combinatorial Problems</li>
</ul>
<h4>
<a id="convex-optimization---problem-space-specification" class="anchor" href="#convex-optimization---problem-space-specification" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Convex Optimization - Problem Space Specification</h4>
<ul>
<li>Convex Sets and Convex Hull</li>
<li>Properties of Convex Sets/Functions</li>
<li>Convex Optimzation Problems</li>
</ul>
<h4>
<a id="numerical-optimization---approaches-and-solutions" class="anchor" href="#numerical-optimization---approaches-and-solutions" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Numerical Optimization - Approaches and Solutions</h4>
<ul>
<li>Newton's Method in Optimization</li>
<li>Higher Dimensions</li>
<li>Wolf Conditions</li>
<li>Armijo Rule and Curvature Condition</li>
<li>Rationale for the Wolfe Conditions</li>
</ul>
<h4>
<a id="constrained-optimization" class="anchor" href="#constrained-optimization" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Constrained Optimization</h4>
<ul>
<li>Definition and Description</li>
<li>General Form</li>
<li>Solution Methods</li>
<li>Constraint Optimization: Branch and Bound</li>
<li>Branch-and-Bound: First Choice Bounding Conditions</li>
<li>Branch and Bound: Russian Doll Search</li>
<li>Branch and Bound: Bucket Elimination</li>
</ul>
<h4>
<a id="lagrange-multipliers" class="anchor" href="#lagrange-multipliers" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Lagrange Multipliers</h4>
<ul>
<li>Problem Formulation</li>
<li>Handling Multiple Constraints</li>
<li>Formulation via Differentiable Manifolds</li>
<li>Interpretation of the Lagrange Multipliers</li>
<li>Sample: Maximal Information Entropy</li>
<li>Sample: Numerical Optimization Techniques</li>
</ul>
<h4>
<a id="karush-kuhn-tucker-conditions" class="anchor" href="#karush-kuhn-tucker-conditions" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Karush-Kuhn-Tucker Conditions</h4>
<ul>
<li>Necessary Conditions for Optimization Problems</li>
<li>Regularity Conditions or Constraint Qualifications</li>
<li>Sufficient Conditions</li>
<li>KKT Conditions Example - Economics</li>
<li>KKT Conditions Example - Value Function</li>
<li>KKT Generalizations</li>
</ul>
<h4>
<a id="interior-point-method" class="anchor" href="#interior-point-method" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Interior Point Method</h4>
<ul>
<li>Interior Point Methodology and Algorithm</li>
</ul>
<h3>
<a id="spline-builder" class="anchor" href="#spline-builder" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spline Builder</h3>
<h4>
<a id="calibration-framework" class="anchor" href="#calibration-framework" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Calibration Framework</h4>
<h4>
<a id="spline-builder-setup" class="anchor" href="#spline-builder-setup" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spline Builder Setup</h4>
<ul>
<li>Design Objective Behind Interpolating Splines</li>
<li>Base Formulation</li>
</ul>
<h4>
<a id="b-splines" class="anchor" href="#b-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>B-Splines</h4>
<ul>
<li>B-Spline Derivatives</li>
</ul>
<h4>
<a id="polynomial-spline-basis-function" class="anchor" href="#polynomial-spline-basis-function" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Polynomial Spline Basis Function</h4>
<ul>
<li>Polynomial SPline Basis Functions</li>
<li>Bernstein Polynomial Basis Functions</li>
</ul>
<h4>
<a id="local-spline-stretches" class="anchor" href="#local-spline-stretches" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Local Spline Stretches</h4>
<ul>
<li>Local Interpolating/Smoothing Spline Stretches</li>
<li>Space Curves and Loops</li>
</ul>
<h4>
<a id="spline-segment-calibration" class="anchor" href="#spline-segment-calibration" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spline Segment Calibration</h4>
<ul>
<li>Smoothing Best Fit Splines</li>
<li>Segment Best Fit Response with Constraint Matching</li>
</ul>
<h4>
<a id="spline-jacobian" class="anchor" href="#spline-jacobian" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Spline Jacobian</h4>
<ul>
<li>Optimizing Spline Basis Function Jacobian</li>
<li>Spline Input Quote Sensitivity Jacobian</li>
</ul>
<h4>
<a id="shape-preserving-spline" class="anchor" href="#shape-preserving-spline" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Shape Preserving Spline</h4>
<ul>
<li>Shape Preserving Tension Spline</li>
<li>Shape Preserving Nu Splines</li>
<li>Alternate Tension Spline Formulations</li>
</ul>
<h4>
<a id="koch-lyche-kvasov-tension-splines" class="anchor" href="#koch-lyche-kvasov-tension-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Koch-Lyche-Kvasov Tension Splines</h4>
<h4>
<a id="smoothing-splines" class="anchor" href="#smoothing-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Smoothing Splines</h4>
<ul>
<li>Penalty Minimization Risk Function</li>
<li>Smoothing Spline Setup</li>
<li>Ensemble Averaging vs. Basis Spline Representation</li>
<li>Least Squares Exact Fit + Curvature + Segment Length Penalty Formulation</li>
<li>Alternate Smootheners</li>
</ul>
<h4>
<a id="multi-dimensional-splines" class="anchor" href="#multi-dimensional-splines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Multi-dimensional Splines</h4>
<h2>
<a id="licence" class="anchor" href="#licence" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Licence</h2>
<p>Apache 2.0</p>
<h2>
<a id="contact" class="anchor" href="#contact" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Contact</h2>
<p><a href="mailto:[email protected]">[email protected]</a></p>
</section>
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