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LGO Global Solver Engine - Advanced Methods

LGO Global Advanced Methods

The research effort leading to the LGO Global Solver Engine -- which was awarded the 2000 INFORMS Computing Society Prize for Research Excellence -- is discussed in the 1996 book Global Optimization in Action by Janos Pinter.  Click here to order it at our online bookstore.

The LGO Global Solver offers a wide range of options and tolerances to control the global optimization process. You can control the tradeoff between rigorous global search and solution time. Options such as Global Convergence, Global Phase Cutoff and Global Phase Iterations allow you to determine when the LGO Global Solver will switch from global to local scope search.

LGO Global Solver Options dialog (36856 bytes)

LGO Global Solver
Options dialog

Handle Almost Any Continuous Function

The LGO Global Solver allows the objective and constraints to be general, convex or non-convex functions -- the only assumption made is that the functions are Lipschitz-continuous.  A function f is Lipschitz-continuous if there exists a constant L > 0, such that for all pairs of points x, y, the absolute value of f(x) - f(y) is no greater than L times the distance between x and y. Among many others, every smooth function (the type handled by the bundled GRG and Large-Scale GRG Solvers) on a closed and bounded set is Lipschitz-continuous.

Use a Full Repertoire of Global and Local Search Methods

The LGO Global Solver includes a full repertoire of global and local scope search methods. The global methods include continuous branch and bound and adaptive random search; the local methods include an exact penalty function approach, a search based on sequential model linearization, and an exact primal (Generalized Reduced Gradient type) nonlinear search algorithm. These methods are invoked sequentially, in a fully automatic mode.

LGO can also be used as a stand-alone nonlinear optimizer (seeking locally optimal solutions) for a wide range of continuous problem functions.

Options for Mixed-Integer Nonlinear Problems

The LGO Global Solver uses the Premium Platform's Branch and Bound method to handle integer variables and "alldifferent" constraints.  If your problem includes integer constraints, you can obtain a quick solution of the relaxation (temporarily ignoring the integer constraints) without having to delete these constraints and then re-enter them later.

You can control the number of Branch and Bound subproblems and the number of integer feasible solutions found before the Solver stops.  And you can speed up the solution of problems with integer constraints by supplying an integer cutoff value -- often known from a previous run.

LGO Global Solver Integer options dialog(19488 bytes)

LGO Global Solver
Integer Options dialog

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