The FICO Xpress optimizer is a commercial

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

solver A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates t ...

for linear programming (LP), mixed integer linear programming (MILP), convex

quadratic programming Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constr ...

(QP), convex quadratically constrained quadratic programming (QCQP),

second-order cone programming A second-order cone program (SOCP) is a convex optimization problem of the form :minimize \ f^T x \ :subject to ::\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m ::Fx = g \ where the problem parameters are f \in \mathbb^n, ...

(SOCP) and their mixed integer counterparts. Xpress includes a general purpose non-linear solver, Xpress NonLinear, including a successive linear programming algorithm (SLP, first-order method), and Artelys Knitro (second-order methods). Xpress was originally developed by Dash Optimization, and was acquired by

FICO FICO (legal name: Fair Isaac Corporation), originally Fair, Isaac and Company, is a data analytics company based in Bozeman, Montana, focused on credit scoring services. It was founded by Bill Fair and Earl Isaac in 1956. Its FICO score, a me ...

in 2008. Its initial authors were Bob Daniel and Robert Ashford. The first version of Xpress could only solve LPs; support for MIPs was added in 1986. Being released in 1983, Xpress was the first commercial LP and MIP solver running on PCs. In 1992, an Xpress version for parallel computing was published, which was extended to distributed computing five years later. Xpress was the first MIP solver to cross the billion matrix non-zero threshold by introducing 64-bit indexing in 2010. Since 2014, Xpress features the first commercial implementation of a parallel dual

simplex method In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are n ...

Technology

Linear and quadratic programs can be solved via the primal simplex method, the dual simplex method or the barrier

interior point method Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1 ...

. All mixed integer programming variants are solved by a combination of the

branch and bound Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate soluti ...

method and the

cutting-plane method In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed ''cuts''. Such procedures are commonly used ...

. Infeasible problems can be analyzed via the IIS (

irreducible In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergence ...

infeasible subset) method. Xpress provides a built-in tuner for automatic tuning of control settings. Xpress includes its modelling language Xpress Mosel and the integrated development environment Xpress Workbench. Mosel includes

distributed computing A distributed system is a system whose components are located on different computer network, networked computers, which communicate and coordinate their actions by message passing, passing messages to one another from any system. Distributed com ...

features to solve multiple scenarios of an optimization problem in parallel. Uncertainty in the input data can be handled via

robust optimization Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the ...

methods. Xpress has a modeling module called BCL (Builder Component Library) that interfaces to the C,

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

programming languages, and to the

.NET Framework The .NET Framework (pronounced as "''dot net"'') is a proprietary software framework developed by Microsoft that runs primarily on Microsoft Windows. It was the predominant implementation of the Common Language Infrastructure (CLI) until bein ...

. Independent of BCL, there are

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

and

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...

interfaces. Next to Mosel, Xpress connects to other standard modeling languages, such as

AIMMS AIMMS (acronym for Advanced Interactive Multidimensional Modeling System) is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore. It has two main product offerings that provide modeling and ...

AMPL AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed ...

, and

GAMS Gams is a municipality in the ''Wahlkreis'' (constituency) of Werdenberg in the canton of St. Gallen in Switzerland. History Gams is first mentioned in 835 as ''Campesias''. In 1210 it was mentioned as ''Chames'', in 1236 as ''Gamps''. Unt ...

. The FICO Xpress Executor"FICO Xpress Executor"
Nov 13, 2018. executes and deploys Mosel models, using

SOAP Soap is a salt of a fatty acid used in a variety of cleansing and lubricating products. In a domestic setting, soaps are surfactants usually used for washing, bathing, and other types of housekeeping. In industrial settings, soaps are use ...

or REST interfaces. It can be used from external applications or from th
FICO Decision Management Platform

References

{{Mathematical optimization software Numerical software Mathematical optimization software