eldo_user

Optimization
Continuous and Discrete Optimization
Optimization Methods
Post-Analysis of Optimization Simulations
Examples of Circuit Optimization
Continuous and Discrete Optimization
In some optimization problems, the variables can only take integer or discrete real values. The
obvious strategy is to ignore the integrality requirement, solving the problem with real
variables. However, rounding all the components to the nearest integer is not guaranteed to
provide an optimal solution. Problems of this type should be handled using discrete
optimization tools. The mathematical formulation is changed by adding the constraint “x i is an
integer for all i in K, where K is a subset of {1, ..., N}”.
Continuous optimization problems are easier to solve. The smoothness of the functions makes it
possible to use function and constraint information at a particular point x to deduce a function’s
behavior at all points close to x.
The same statement cannot be made about discrete problems where nearby points may have
markedly different function values. Moreover, the set of possible solutions is too large to make
an exhaustive search for the best value in this finite set. Models that contain some variables
which are allowed to vary continuously and others that can attain only integer values are
referred to as mixed-integer programming problems (MIP).
The Eldo optimizer can only handle non-linear problems (NLP) with continuous variables. The
increment parameter in the .PARAMOPT command is used to define a grid of feasible integer
points with uniform steps. A strategy is used which ignores the discretization requirement—it
solves the problem with real variables and then rounds all the components to the nearest point
onto the grid at the end of optimization. This strategy is based on the assumption that the
increment value is sufficiently small. The problem solved by the optimizer is a continuous
relaxation of the original MIP problem where the constraints of integrality on variables are
simply relaxed.
Related Topics
Global and Local Optimization
Smooth and Non-Smooth Problems
Multiple-Run Compatibility
Optimization of Sweep Simulations
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Eldo® User's Manual, 15.3