A Golomb Ruler (GR) is a set of integer marks along an imaginary ruler such that all the distances of the marks are different. Computing a minimum length GR is associated with many applications (from astronomy to information theory). Recently we proposed a new continuous optimization model for the problem, and based on a given theoretical result and some computational experiments, we conjecture that an optimal solution of this model is also a solution to an associated GR of minimum length. Costas Arrays are, in some way, a generalization of the GR in dimension two. A Costas Array is an n × n array of dots and blanks with exactly one dot in each row and column, such that the vector displacement between any pair of dots is distinct. The literature describes constructive algebraic methods to find the Costas array. Costas array has applications in radar engineering and experimental design. We answer some open questions on the Costas array using a continuous optimization model to obtain all Costas Arrays for each n. Computational experiments illustrate that our approach is feasible.