The minimum covering lp-hypersphere problem is defined as to find an lp-hypersphere of minimum radius enclosing a finite set of given points in ℝn. An lp-hypersphere is defined as a set Sp(c,r)={x∈ℝn:lp(x-c)∈r∈, where c is a point in ℝn, called the center of Sp, r is a positive number, called the radius of Sp, and lp is the lp-norm, l∈p∈¸∈. The authors study some primal and dual algorithms for this problem which are based in the feasible directions method and in the Wolfe duality theory. Computational results are given showing that the proposed algorithms can be used to approximate the optimal solution for large problems. Improvements of Elzinga and Hearn’s algorithm, given p=2, are also given.
