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  2. List of optimization software - Wikipedia

    en.wikipedia.org/wiki/List_of_optimization_software

    MIDACO – a software package for numerical optimization based on evolutionary computing. MINTO – integer programming solver using branch and bound algorithm; freeware for personal use. MOSEK – a large scale optimization software. Solves linear, quadratic, conic and convex nonlinear, continuous and integer optimization.

  3. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    A number of algorithms for other types of optimization problems work by solving linear programming problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations.

  4. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    Big M method. In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints. It does so by associating the constraints with large negative constants which would not be part of any optimal ...

  5. Interior-point method - Wikipedia

    en.wikipedia.org/wiki/Interior-point_method

    Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms: Theoretically, their run-time is polynomial —in contrast to the simplex method, which has exponential run-time in the worst case.

  6. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment. Otherwise, it is called unbalanced assignment. [1] If the total cost of the assignment for all ...

  7. Branch and bound - Wikipedia

    en.wikipedia.org/wiki/Branch_and_bound

    Branch and bound. Branch and bound ( BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as ...

  8. OR-Tools - Wikipedia

    en.wikipedia.org/wiki/OR-Tools

    Google OR-Tools is a free and open-source software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related optimization problems. OR-Tools is a set of components written in C++ but provides wrappers for Java, .NET and Python.

  9. Slack variable - Wikipedia

    en.wikipedia.org/wiki/Slack_variable

    In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality constraint. A non-negativity constraint on the slack variable is also added.: 131 Slack variables are used in particular in linear programming.

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