Techniques for exploring the suboptimal set
Optimization and Engineering, 11(2):319-337, June 2010.
The 
-suboptimal set 
for an optimization problem is
the set of feasible points with objective value within
of optimal.
In this paper we describe some basic techniques for quantitatively
characterizing , for a given value of ,
when the original problem is convex,
by solving a modest number of related convex optimization problems.
We give methods for computing the bounding box of ,
estimating its diameter, and forming ellipsoidal approximations.
Quantitative knowledge of can be very useful
in applications.
In a design problem, where the objective function is some cost,
large is good:
It means that there are many designs with nearly
minimum cost, and we can use this design freedom to improve a
secondary objective.
In an estimation problem,
where the objective function is some measure of plausibility,
large is bad: It means that quite different
parameter values are almost as plausible as the most plausible
parameter value.