The Gurobi Optimizer is a state-of-the-art solver for linear programming (LP), quadratic programming (QP) and mixed-integer programming (MILP and MIQP). It was designed from the ground up to exploit modern multi-core processors. Every Gurobi license allows parallel processing, and the Gurobi Parallel Optimizer is deterministic: two separate runs on the same model will produce identical solution paths. For solving LP and QP models, the Gurobi Optimizer includes high-performance implementations of the primal simplex method, the dual simplex method, and a parallel barrier solver. For MILP and MIQP models, the Gurobi Optimizer incorporates the latest methods including cutting planes and powerful solution heuristics. All models benefit from advanced presolve methods to simplify models and slash solve times. The Gurobi Optimizer is written in C and is accessible from several languages. In addition to a powerful, interactive Python interface and a matrix-oriented C interface, we provide object-oriented interfaces from C++, Java, Python, and the .NET languages. These interfaces have all been designed to be lightweight and easy to use, with the goal of greatly enhancing the accessibility of our products. And since the interfaces are lightweight, they are faster and use less memory than other standard interfaces. Our online documentation (Quick Start Guide, Example Tour and Reference Manual) describes the use of these interfaces. Gurobi is also available through several powerful third-party modeling systems including AIMMS, AMPL, FRONTLINE SOLVERS, GAMS, MPL, OptimJ and TOMLAB. Version 4.0 of the Gurobi Optimizer includes a number of enhancements. Users of previous versions may need to make a few minor changes to their existing programs. Here are the new features, and the likely changes required to existing programs. New features: * Quadratic programming: The Gurobi Optimizer now supports models with quadratic objective functions. The new version includes primal simplex, dual simplex, and parallel barrier optimizers for continuous QP models, and a parallel branch-and-cut solver for Mixed Integer Quadratic Programming (MIQP) models. * Concurrent optimizer: The Gurobi Optimizer now allows you to run multiple algorithms simultaneously when solving a linear continuous model on a multi-core machine. The optimizer returns when the first algorithm solves the model. We include both a standard concurrent optimizer and a deterministic concurrent optimizer. The latter returns the exact same solution every time you run it, while the former can sometimes return different optimal solutions from one run to the next. The former can sometimes be significantly faster. * MIP performance: The MIP solver is faster in release 4.0. These improvements do not require any parameter changes. * LP performance: The simplex and barrier solvers are slightly faster in release 4.0. We have also improved the numerical stability of the primal simplex solver and the barrier crossover algorithm. * Delayed MIP strategy change: The Gurobi Optimizer now gives you the option to change a few MIP parameters in the middle of the optimization in order to dynamically shift the search strategy. Specifically, two new parameters, ImproveStartGap and ImproveStartTime, allow you to specify when the algorithm should modify the values of a few parameters that control the intensity of the MIP heuristics. By setting one or both of these parameters to non-default values, you can cause the MIP solver to switch from its standard parameter settings, where it tries to strike a balance between finding better solutions and proving that the current solution is optimal, to a set of parameter values that focus almost entirely on finding better solutions. * Support for Visual Studio 2010: Gurobi Optimizer now supports Microsoft Visual Studio 2010. This change only affects C++ users, who will find new libraries gurobi_c++2010md.lib, gurobi_c++2010mdd.lib, gurobi_c++2010mt.lib, and gurobi_c++2010mtd.lib in the lib directory of the Gurobi distribution. * Explicit license release in Java and .NET: The new version includes an explicit method for releasing a Gurobi license. You no longer need to rely on the garbage collector to reclaim unused licenses. * New methods, attributes, parameters, and error codes: To support the new features in Gurobi 4.0, we have added several new methods, attributes, parameters, and error codes. You can learn more about these in the {Gurobi Reference Manual}. New methods: * New C methods for managing Q: the C interface includes three new routines, GRBaddqpterms, GRBdelq, and GRBgetq. These allow you to add, delete, and retrieve quadratic objective terms, respectively. * Quadratic expressions: the object oriented interfaces include a new quadratic expression class, GRBQuadExpr, which can be used to build quadratic objective functions. * getObjective/setObjective: the object oriented interfaces include new GRBModel methods that allow you to retrieve the current objective function as a linear or quadratic expression, and allow you to set the objective equal to a linear or quadratic expression. * getValue: the object oriented interfaces include a new getValue method that allows you to compute the value of a GRBLinExpr or GRBQuadExpr object for the current solution. * License release: the Java and .NET interfaces include a new release method that allows you to release the license held by an environment immediately, instead of having to wait for the garbage collector to reclaim the GRBEnv object. New attributes: * IsQP: model attribute that indicates whether the model has any quadratic terms. * NumQNZs: model attribute that returns the number of quadratic terms in the objective function. New parameters: * Method: the previous LPMethod parameter has been renamed to Method. This new parameter controls the algorithm used to solve continuous linear and quadratic models. We have added two new options: concurrent and deterministic concurrent. This parameter also selects the algorithm used to solve the root node of a MIP model. * NodeMethod: chooses the algorithm used to solve node relaxations in a MIP model. * ModKCuts: controls the generation of mod-k cuts. * ImproveStartGap: allows you to specify the optimality gap at which the MIP solver resets a few MIP heuristics parameters in order to shift the attention of the MIP solver to finding the best possible feasible solution. * ImproveStartTime: allows you to specify the elapsed time at which the MIP solver resets a few MIP heuristics parameters in order to shift the attention of the MIP solver to finding the best possible feasible solution. * PreMIQPMethod: chooses the presolve transformation performed on MIQP models. * PSDTol: sets a limit on the amount of diagonal perturbation that the optimizer is allowed to do on the Q matrix for a quadratic model. If a larger perturbation is required, the optimizer will terminate with an GRB_ERROR_Q_NOT_PSD error. New error codes: * GRB_ERROR_Q_NOT_PSD: This new error code is returned when you attempt to solve a QP model where the Q matrix is not positive semi-definite (meaning there exists an x for which x'Qx ). Note that the optimizer will always