SQP method for NLP

Sequential quadratic programming (SQP) is a popular method for solving nonlinear programming problems. The ALGLIB nonlinear programming suite includes one of the fastest open-source SQP implementations (see the benchmark) as well as other nonlinear programming algorithms. These are available in C++, C#, Java and several other programming languages under a dual free/commercial licensing model.

This article discusses the specifics of the SQP solver. A high-level overview of the ALGLIB nonlinear programming suite is provided on another page. If you found this page while looking for a quadratic programming solver, ALGLIB also offers one.

ALGLIB SQP solver overview

Features

The smooth nonlinear programming functionality in ALGLIB is provided by the minnlc subpackage of the Optimization package. The ALGLIB implementation of the Sequential Quadratic Programming algorithm includes many performance and stability improvements:

• A sparse version scalable to problems with tens of thousands of variables and sparse constraints (and/or limited amount of dense constraints)
• A dense version which provides better performance for problems with many dense constraints
• Parallel numerical differentiation
• A filter method to accelerate convergence
• The ability to recover from the target function breakdown (the algorithm tries to avoid areas where target returns NAN/INF)
• No parameters to tune

The solver has nice convergence requirements (C1 continuity of the target/constraints, no convexity requirements) and can handle infeasible initial points. It is one of the fastest open-source optimizers available!

Programming languages supported

ALGLIB supports many programming languages, including C++, C#, Java, Python, and others:

• C++ version. Highly optimized, portable (x86/x64/ARM, works on Windows, Linux, and POSIX systems), and is a self-contained library
• C# version. Unified C# API for two backends - a fully managed C# implementation and a high-performance native computational core written in C
• Java, Python and other languages. A wrapper for a high-performance native computational core written in C. Seamless integration with the target programming language

A distinctive feature of ALGLIB is that it provides exactly the same API in all programming languages. This is achieved with our exclusive technology of automatic code translation and wrapper generation.

Comparison with other open-source solvers

In order to evaluate the performance and robustness of our NLP solvers we compared our SQP implementation with several open-source nonlinear programming solvers using a subset of the CUTEst test problem set (see the smooth NLP benchmark page for a more detailed discussion).

The result is that ALGLIB is consistently faster and more robust that other open-source solvers.

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