Welcome to Irene’s documentation!

Contents:

• Introduction
  • Documentation Scope
  • Requirements and dependencies
  • Download
  • Installation
  • License
• Architecture and Method Guide
  • From Polynomial Expressions to Group-Rings
  • Module Layers
  • Choosing a Relaxation Family
  • Typical Workflow
• Group-Ring Foundations
  • Algebraic Setting
  • Commutative Semigroup and Semigroup Algebra
  • Support and Geometry
  • Differential Operators
  • Why This Matters for POP
• Problem Representation
  • Problem Template
  • Core Responsibilities
  • Degree Conventions
  • Key Methods
  • From Equations to Methods
  • Delta Sets and Newton Data
  • Minimal Construction Pattern
• Semidefinite Programming
  • Primal and Dual formulations
  • The sdp class
• Optimization
  • Notation Bridge to Geometric and SONC Chapters
  • Beyond SDP: Alternative Lower-Bound Mechanisms
  • Moment Constraints
  • Equality Constraints
  • Extracting solutions
• Geometric Programming Relaxations
  • Theory to Implementation
  • Interpretation of the Matrix Transform
  • Constraint Families in solve
  • Lower-Bound Meaning
  • Practical Notes
• SONC Relaxations
  • Formulation Focus
  • Variable Roles
  • Branching on \(\lambda_0^{(\beta)}\)
  • Implementation Stages in SONCRelaxations
  • Theory-to-Code Anchors
  • Geometric Interpretation
  • Repository Anchors
• Approximating Optimum Value
  • Using pyProximation.OrthSystem
• Benchmark Optimization Problems
  • Rosenbrock Function
  • Giunta Function
  • Parsopoulos Function
  • Shubert Function
  • McCormick Function
  • Schaffer Function N.2
  • Schaffer Function N.4
  • Drop-Wave Function
• Examples and Validation
  • Recommended Example Sequence
  • API Quick Reference
  • SDP Example
  • Geometric Programming Example
  • SONC Examples
  • Example 3.3 Traceability
  • Regression Validation
• Code Documentation
  • LaTeX()
  • base
  • Calpha_()
  • Calpha__()
  • Mom
  • SDPRelaxations
  • SDRelaxSol
  • sdp
  • OptimizationProblem
  • AtomicSGElement
  • CommutativeSemigroup
  • SemigroupAlgebra
  • SemigroupAlgebraElement
  • GPRelaxations
  • SONCRelaxations

pyProximation

• pyProximation (lean)
  • Requirements and dependencies
  • Download
  • Installation
  • License
• Measures
  • Density function
  • Integrals
  • p-norms
  • Drawing samples
• Hilbert Spaces
  • Orthonormal system of functions
  • OrthSystem
  • Approximation
  • Rational Approximation
• Interpolation
  • Lagrange interpolation
  • \(L^2\)-approximation with discrete measures
• Code Documentation
  • Foundation
  • Measure
  • OrthSystem
  • RationalApprox
  • RationalAprox
  • Interpolation

Reference

• Revision History
• To Do
  • Done
• Appendix
  • pyProximation
  • pyOpt
  • LaTeX support

Indices and tables

• Index

• Module Index

• Search Page