This is an implementation of the algorithm proposed by Harman et al. (2016); see the references. The inequalities A%*%w<=b, w0<=w with the specific properties mentioned above, form the so-called resource constraints. They encompass many practical restrictions on the design, and lead to a bounded set of feasible solutions.
The information matrix of w1 should preferably have the reciprocal condition number of at least 1e-5. Note that the floor of an optimal approximate design (computed for instance using od_MISOCP) is often a good initial design. Alternatively, the initial design can be the result of another optimal design procedure, such as od_AQUA. Even if no initial design is provided, the model should be non-singular in the sense that there exists an exact design w with a well conditioned information matrix, satisfying all constraints. If this requirement is not satisfied, the computation may fail, or it may produce a deficient design.
The procedure always returns a permissible design, but in some cases, especially if t.max is too small, the resulting design can be inefficient. The performance depends on the problem and on the hardware used, but in most cases the function can compute a nearly-optimal exact design for a problem with a few hundreds design points and tens of constraints within minutes of computing time. Because this is a heuristic method, we advise the user to verify the quality of the resulting design by comparing it to the result of an alternative method (such as od_AQUA and od_MISOCP) and/or by computing its efficiency relative to the corresponding optimal approximate design.
In the very special (but frequently used) case of the single constraint on the experimental size, it is generally more efficient to use the function od_KL.