I am interested in understanding the types of optimization problems OpenOpt was designed to solve and how to get started with its installation. Please list three distinct problem types from the 'Problems Tree' that OpenOpt could handle, and then navigate to the 'Install' page to identify the primary programming language required and any specific installation commands or prerequisites mentioned.
Navigate to the OpenOpt homepage (openopt.org). Click on the 'Problems Tree' link (ID 22). Identify and list three distinct problem types from the 'Problems Tree'. Navigate back to the homepage. Click on the 'Install' link (ID 16). Identify the primary programming language required for OpenOpt. Identify any specific installation commands or prerequisites mentioned on the 'Install' page. Synthesize the collected information into a concise answer.
Successfully navigate to the 'Problems Tree' page. List three distinct problem types, such as 'LP (Linear Programming)', 'QP (Quadratic Programming)', 'MILP (Mixed-Integer Linear Programming)', 'MINLP (Mixed-Integer Nonlinear Programming)', 'GLP (Global Optimization)', 'SNLE (System of Nonlinear Equations)', 'ODE (Ordinary Differential Equations)', 'EIG (Eigenvalue problems)', 'NSP (Non-Smooth Programming)', 'TSP (Travelling Salesman Problem)', 'MCP (Mixed Complementarity Problem)', 'SOCP (Second-Order Cone Programming)', 'SDP (Semidefinite Programming)', 'CVX (Convex Optimization)', 'NLP (Nonlinear Programming)', 'LLSP (Linear Least Squares Problem)', 'LS (Least Squares)', 'LSP (Linear Programming with Sparse Matrix)', 'QCP (Quadratic Constrained Programming)', 'TRP (Trust Region Problem)', 'DCP (Discrete Convex Programming)', 'MOP (Multi-Objective Programming)', 'ISP (Integer Semi-Definite Programming)', 'CSP (Constraint Satisfaction Problem)', 'SCP (Set Covering Problem)', 'VRP (Vehicle Routing Problem)'. Successfully navigate to the 'Install' page. State that the primary programming language required is Python. Mention that installation involves using `pip` (e.g., `pip install openopt`) or downloading from a repository (e.g., SVN) and running `python setup.py install`.