CVXOPT
CVXOPT is a free software package for convex optimization based on the Python programming language. It can be used with the interactive Python interpreter, on the command line by executing Python scripts, or integrated in other software via Python extension modules. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python’s extensive standard library and on the strengths of Python as a high-level programming language. Efficient Python classes for dense and sparse matrices (real and complex), with Python indexing and slicing and overloaded operations for matrix arithmetic. Interfaces to the linear programming solver in GLPK, the semidefinite programming solver in DSDP5, and the linear, quadratic and second-order cone programming solvers in MOSEK.
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AMPL
AMPL is a powerful and intuitive modeling language designed to represent and solve complex optimization problems. It enables users to formulate mathematical models in a syntax that closely mirrors algebraic notation, facilitating a clear and concise representation of variables, objectives, and constraints. AMPL supports a wide range of problem types, including linear programming, nonlinear programming, mixed-integer programming, and more. One of its key strengths is the ability to separate models and data, allowing for flexibility and scalability in handling large-scale problems. The platform offers seamless integration with numerous solvers, both commercial and open-source, providing users with the flexibility to choose the most appropriate solver for their specific needs. AMPL is available across multiple operating systems, including Windows, macOS, and Linux, and offers various licensing options.
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Analytic Solver
Analytic Solver Optimization - 100% upward compatible from the Excel Solver - handles every type and size of the conventional optimization problem (without uncertainty). Unlike other optimization software, it algebraically analyzes your model structure and maximally exploits multiple cores in your PC. You can solve nonlinear models 10 times larger, and linear models 40 times larger than the Excel Solver, get solutions much faster – and plug-in Solver Engines to handle up to millions of variables! Analytic Solver Simulation gives you easy-to-use, powerful Monte Carlo simulation and risk analysis, decision trees, and simulation optimization using Frontline’s advanced Evolutionary Solver. With 60 probability distributions plus compound distributions, automatic distribution fitting, rank-order and copula-based correlation, 80 statistics, risk measures and Six Sigma functions, multiple parameterized simulations and more.
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Artelys Knitro
Artelys Knitro is a leading solver for large-scale nonlinear optimization problems, offering a suite of advanced algorithms and features to address complex challenges across various industries. It provides four state-of-the-art algorithms: two interior-point/barrier methods and two active-set/sequential quadratic programming methods, enabling efficient and robust solutions for a wide range of optimization problems. Additionally, Knitro includes three algorithms specifically designed for mixed-integer nonlinear programming, incorporating heuristics, cutting planes, and branching rules to effectively handle discrete variables. Key features of Knitro encompass parallel multi-start capabilities for global optimization, automatic and parallel tuning of option settings, and smart initialization strategies for rapid infeasibility detection. The solver supports various interfaces, including object-oriented APIs for C++, C#, Java, and Python.
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