## Powerful LINDO API solvers

LINDO API includes a set of built-in solvers to tackle a wide variety of problems. It offers increased control of the algorithms and solver parameters. This allows the user to customize the solution strategy to individual applications to achieve optimal control and speed.

## Linear Solvers

The LINDO API is available with three state of the art solvers for linear models.

## Primal and Dual Simplex Solvers

The base version includes the Primal and Dual Simplex solvers, which incorporate numerous enhancements for maximum speed and robustness. Pricing options, for instance, include partial pricing and Devex. You have the option to choose the best pricing strategy based upon problem characteristics.

## Barrier Solver

The optional Barrier solver provides an alternative means of solving linear models. The Barrier option utilizes a barrier or interior point method to solve linear models. Unlike the Simplex solvers that move along the exterior of the feasible region, the Barrier solver moves through the interior space to find the optimum. Depending upon the size and structure of a particular model, the Barrier solver may be significantly faster than the Simplex solvers and can provide exceptional speed on large linear models -- particularly on sparse models with more than 5,000 constraints or highly degenerate models. The Barrier license option is required to utilize the Barrier solver.

## Integer Solver

For models with general and binary integer restrictions, LINDO API includes an integer solver that works in conjunction with the linear, nonlinear and quadratic solver. For linear models, you have the ability to tailor the solution strategy and apply different classes of cuts to ensure maximum speed on particular problem structures.

## Nonlinear Solvers

LINDO API is the first full-featured callable solver to offer general nonlinear capabilities. LINDO API includes a number of ways to find locally or globally optimal solutions to nonlinear models.

## General Nonlinear Solver

For nonlinear programming models, the primary underlying technique used by LINDO API's optional nonlinear solver is based upon a Generalized Reduced Gradient (GRG) algorithm. However, to help get to a good feasible solution quickly, LINDO API also incorporates Successive Linear Programming (SLP). The nonlinear solvertakes advantage of sparsity for improved speed and more efficient memory usage. The Nonlinear license option is required to solve nonlinear models.

## Global Solver

Local search solvers are generally designed to search only until they have identified a local optimum. If the model is non-convex, other local optima may exist that yield significantly better solutions. Rather than stopping after the first local optimum is found, the Global solver will search until the global optimum is confirmed. The Global solver converts the original non-convex, nonlinear problem into several convex, linear subproblems. Then, it uses the branch-and-bound technique to exhaustively search over these subproblems for the global solution. The Nonlinear and Global license options are required to utilize the global optimization capabilities.

## Multistart Solver

When limited time makes searching for the global optimum prohibitive, the Multistart solver can be a powerful tool for finding good solutions more quickly. This intelligently generates a set of candidate starting points in the solution space. Then, the general nonlinear solver intelligently selects a subset of these to initialize a series of local optimizations. For non-convex nonlinear models, the quality of the solution returned by the multistart solver will be superior to that of the general nonlinear solver. The Nonlinear and Global license options are required to utilize the multistart capabilities.

## Quadratic Solver

In addition to solving linear and mixed integer models, with the Barrier option LINDO API can automatically detect and solve models in which the objective function and/or some constraints include quadratic terms. By taking advantage of the quadratic structure, LINDO API can solve these models much more quickly than using the general nonlinear solver. LINDO API can even handle quadratic models with binary and general integer restrictions. These quadratic capabilities make LINDO API suitable for applications such as portfolio optimization problems, constrained regression problems, and certain classes of difficult logistics problems (e.g., layout problems, fixed-charge-network problems with quadratic objectives). The Quadratic solver is included in the Barrier license option.

## Conic Solver

The Conic option for LINDO API includes a Conic solver to efficiently solve Second Order Cone Problems (SOCP). By expressing certain nonlinear models as SOCPs, the Conic solver can be used to solve the model substantially faster than the general nonlinear solver. The Barrier and Conic options are required to utilize the Conic solver.

## Stochastic Programming Solver

Incorporate risk into multi-stage optimization models, maximize expected profit, and summarize results in histograms showing the distribution of possible profit, etc. This new option allows modeling and optimization for models with uncertain elements via multistage stochastic linear, nonlinear and integer stochastic programming (SP). Benders decomposition is used for solving large linear SP models. Deterministic equivalent method is used for solving nonlinear and integer SP models. Support is available for over 20 distribution types (discrete or continuous). The Stochastic Programming solver is included in the Stochastic Programming option.

## Preprocessing and User Control

Preprocessing routines are included in all solvers. The Linear and Nonlinear solvers include scaling and model reduction techniques. Scaling procedures can improve speed and robustness on numerically difficult models. Model reduction techniques can often make models solve faster by analyzing the original formulation and mathematically condensing it into a smaller problem. The Integer solver includes extensive preprocessing and cut generation routines.

LINDO API is designed, so the user has as much control over the input to the solvers as possible. When the Solve routine is initiated, LINDO API analyzes the problem and considers internal parameters set by the user to achieve optimal performance for your particular problem.

## Linearization

LINDO API's Linearization cap common nonsmooth functions. The feature can automatically convert many nonsmooth functions and operators (e.g., max and absolute value) to a series of linear, mathematically equivalent expressions. Many nonsmooth models may be entirely linearized. This allows the linear solver to quickly find a global solution to what would have otherwise been and intractable problem.