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da.p7core.gtopt

3. GTOpt

This part of the pSeven Core manual is a guide to the Generic Tool for Optimization (GTOpt).

• 3.1. Introduction
• 3.2. Definitions
  • 3.2.1. Problem Statement
  • 3.2.2. Optimal Solution
  • 3.2.3. Optimal and Infeasible Result Sets
  • 3.2.4. Assumptions on Objectives and Constraints
• 3.3. Supported Problem Types
  • 3.3.1. Overview
  • 3.3.2. Linear Problems
  • 3.3.3. Quadratic Problems
  • 3.3.4. Box Constrained Single-Objective Problems
  • 3.3.5. Single-Objective Constrained Problems
  • 3.3.6. Constraint Satisfaction Problems
  • 3.3.7. Multi-Objective Optimization
    • 3.3.7.1. Overview
    • 3.3.7.2. Technical Details
  • 3.3.8. Data Fitting Problem
  • 3.3.9. Mixed Integer Variables
  • 3.3.10. Solver Architecture
    • 3.3.10.1. Input Problem Representation
    • 3.3.10.2. Adapter to Optimizer Pairing
    • 3.3.10.3. Optimization Manager
    • 3.3.10.4. Optimization Tree
    • 3.3.10.5. Example
• 3.4. Noisy Problems
  • 3.4.1. Noisy vs Meaningless Problems
  • 3.4.2. Accepted Noise Model
  • 3.4.3. Framed Gradients
    • 3.4.3.1. General Ideas
    • 3.4.3.2. Technical Details
  • 3.4.4. Summary
• 3.5. Numerical Methods
  • 3.5.1. General
  • 3.5.2. Multi-Objective Descent
    • 3.5.2.1. Optimal Descent
    • 3.5.2.2. Quasi-Newton Descent
• 3.6. Termination Criteria
  • 3.6.1. Convergence Criteria
  • 3.6.2. Feasibility
• 3.7. Robust Optimization
  • 3.7.1. Overview
  • 3.7.2. Quantitative Discussion
    • 3.7.2.1. Robust Problem Formulation
    • 3.7.2.2. Approximated Problem
    • 3.7.2.3. Approximated Problem Solution
    • 3.7.2.4. Efficient Sample Size Selection
    • 3.7.2.5. Chance Constraints Treatment
    • 3.7.2.6. Robust Problem Optimal Solution
    • 3.7.2.7. Notes on Statistics Estimation
    • 3.7.2.8. Mean Variance Optimization
    • 3.7.2.9. Illustrative Examples
  • 3.7.3. Notes on Surrogate Based Robust Optimization
  • 3.7.4. Using Stochastic Variables
• 3.8. Surrogate Based Optimization
  • 3.8.1. SBO in GTOpt
  • 3.8.2. Overview
  • 3.8.3. Single-Objective Constrained SBO
  • 3.8.4. Multi-Objective Constrained SBO
  • 3.8.5. Parallel SBO
  • 3.8.6. High-Dimensional SBO
  • 3.8.7. Direct SBO
  • 3.8.8. Summary
• 3.9. Optimization Workflow
  • 3.9.1. Problem Investigation
    • 3.9.1.1. Performance Measures
    • 3.9.1.2. Selecting Design Variables
    • 3.9.1.3. Selecting Constraints
    • 3.9.1.4. Generic and Box Constraints
    • 3.9.1.5. Selecting Uncertain Parameters
  • 3.9.2. Local and Global Methods
    • 3.9.2.1. Local Methods
    • 3.9.2.2. Global Methods
    • 3.9.2.3. GTOpt Strategy
    • 3.9.2.4. Usage Notes
  • 3.9.3. Preliminary Study
    • 3.9.3.1. Large Scale Study
    • 3.9.3.2. Small Scale Properties
  • 3.9.4. Problem Solving
• 3.10. Option Reference
• 3.11. Hint Reference