E-mail this pageThe Lipschitz-continuous Global Optimizer (LGO) software system integrates global and local solvers, to handle nonlinear programming models of the general form min f(x) where the decision vector x belongs to the feasible set D. The feasible set is defined by component-wise finite lower and upper bonds l, u, and by an optional vector function of constraints g(x). That is, D={x: l ≤ x ≤ u, g(x) ≤ 0}. In contrast to several widely used nonlinear local optimization solver engines (such as CONOPT or MINOS), LGO's main scope of application is global optimization. However, LGO also has its own built-in local nonlinear optimization capability.
An important point to emphasize is that model sparsity or other special model structure are not assumed or exploited by LGO. Hence, nonlinear models handled by LGO can be defined by arbitrary computable functions that – for reasons of theoretical validation of the numerical results obtained – should be continuous or Lipschitz-continuous over a given finite “box” range of the (continuous) decision variables. These mild analytical requirements are met by many practical models. Without going into details, note that, for example all models defined by continuously differentiable functions on the range [l,u] have a suitable Lipschitz structure (and of course are also continuous). 
The LGO integrated global-local nonlinear solver suite extends your modeling/solving capability, with support for using arbitrary continuous functions in your AIMMS model formulation. Some prominent examples are sin, cos, tan, abs, min, max, together with many other functions. LGO can handle constraints with a reference to an external function and is considered to be a one-step solution to handle dense continuous nonlinear models globally and locally, without further restrictions.
LGO Usage
LGO’s search algorithms can be used for models up to 5,000 variables and 3,000 constraints.
Website: www.pinterconsulting.com
Version(s): AIMMS supports LGO 1.0. Also available in free trial license of AIMMS.
AIMMS/LGO References:
- AIMMS/LGO Solver Engine - A Brief Introduction and User’s Guide by János D. Pintér, Pintér Consulting Services, 2005.
- Nonlinear Systems Modeling and Optimization Using AIMMS/LGO by János D. Pintér, Pintér Consulting Services, 2006.
LGO References:
- Global Optimization in Action -Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications by János D. Pintér, Pinter Consulting Services, 1996 (Springer, ISBN: 0-7923-3757-3).
- Computational Global Optimization in Nonlinear Systems - An Interactive Tutorial by János D. Pintér, Pintér Consulting Services, 2001. (Lionheart Publishing, ISBN: 1-931634-02-5).
- Global Optimization - Scientific and Engineering Case Studies Edited by János D. Pintér, Pintér Consulting Services, 2006. (Springer, ISBN: 0-387-30408-8).
