The Maple Global Optimization Toolbox is an add-on software module for Maple that provides advanced global optimization algorithms to find the best possible solution to complex nonlinear models, even in the presence of multiple local optima. It integrates seamlessly with Maple’s numeric and symbolic computation environment and supports both command-line and interactive usage for defining, solving, and visualizing optimization problems.

Key Features

Multiple Global Search Algorithms Robust suite of algorithms for global optimization.

• Branch-and-bound global search for Lipschitz-continuous models
• Adaptive random search and multi-start stochastic search for general nonlinear problems

Local Search Integration Combines global and local methods for refined solutions.

• Generalized reduced gradient local search for final solution refinement
• Option to disable global search and use local search only

Support for Complex Models Handles a wide range of mathematical functions and constraints.

• Accepts arbitrary objective and constraint functions, including special functions, derivatives, integrals, and Maple procedures
• Solves problems with thousands of variables and constraints

Interactive and Command-Line Interfaces Flexible user interaction modes.

• Global Optimization Assistant for easy problem setup and visualization
• Command-line interface for advanced users and automation

Visualization Tools Comprehensive model visualization within Maple.

• 1D and 2D subspace projections of objective functions and constraints
• Plots of solution regions and constraint surfaces

Precision and Stability High accuracy in solutions.

• Utilizes Maple’s arbitrary precision capabilities to reduce numerical instability

Benefits

Finds True Global Optima Ensures the best solution is found, not just a local optimum.

• Avoids sub-optimal solutions common in local-only methods
• Suitable for engineering, science, and business models with multiple local minima/maxima

Integrated with Maple Leverages Maple’s symbolic and numeric power.

• Direct use of Maple’s mathematical modeling and documentation tools
• Seamless workflow for model development, solution, and result visualization

User-Friendly and Flexible Accessible for both beginners and advanced users.

• Interactive assistant simplifies setup for non-experts
• Command-line and matrix input for power users and large-scale problems