Introduction to Global Optimization, Lipschitz-Continuous Global Optimizer

1 Introduction

1.1 Overview

Welcome to the TOMLAB /LGO User's Guide. TOMLAB /LGO includes the LGO solver from Pintér Consulting Services and an interface to MATLAB, by MathWorks'.

The Lipschitz-Continuous Global Optimizer (LGO) solver suite serves for the analysis and global solution of general nonlinear programming (NLP) models. The LGO solver system has been developed and gradually extended for more than a decade and it now incorporates a suite of robust and efficient global and local nonlinear solvers. It can also handle smaller LP models. LGO is documented elsewhere in detail: see for example, Pintér (1996, 2001, 2003). [1, 2, 3]

TOMLAB /LGO integrates the following global scope algorithms:

Branch-and-bound (adaptive partition and sampling) based global search (BB)
Adaptive global random search (GARS)
Adaptive multistart global random search (MS)

LGO also includes the following local solver strategies:

Constrained local search, based on a generalized reduced gradient approach (GRG).

The overall solution approach followed by TOMLAB /LGO is based on the seamless combination of the global and local search strategies. This allows for a broad range of operations. In particular, a solver suite approach supports the flexible usage of the component solvers: one can execute fully automatic (global and/or local search based) optimization, and can design customized interactive runs.

TOMLAB /LGO does not rely on any sub-solvers, and it does not require any in-depth structural information about the model. It is particularly suited to solve even 'black box' (closed, confidential), or other complex models, in which the available analytical information may be limited. TOMLAB /LGO needs only computable function values (without a need for higher order analytical information). TOMLAB /LGO can even solve models having constraints involving continuous, but non-differentiable functions. Thus, within TOMLAB, LGO is well suited to solve nonlinear - global and convex - optimization models.

TOMLAB /LGO can also be used in conjunction with other TOMLAB solvers. Local solvers (when available) can be used to verify the solution found by LGO, and to provide additional local information.

1.2 Contents of this manual

Section 1 provides a basic overview of the TOMLAB /LGO solver package.
Section 2 provides an overview of the Matlab interface to LGO.
Section 3 describes how to set LGO solver options from Matlab.
Section 4 provides information regarding TOMLAB /LGO test examples.
Section 5 gives detailed information about the interface routine lgoTL.

1.3 More information

Please visit the following links for more information and see the illustrative references at the end of this manual.

http://tomopt.com/tomlab/products/lgo/

1.4 Prerequisites

In this concise manual we assume that the user is familiar with global optimization and nonlinear programming, setting up problems in TOMLAB (in particular global constrained nonlinear (glc) problems) and with the Matlab language in general.

« Previous « Start » Next »