Solving non-monotone equilibrium problems via a DIRECT-type approach

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of … Read more

A modified DIRECT algorithm for a problem in astrophysics

We present a modification of the DIRECT algorithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema … Read more

Toward a new DIRECT algorithm. A two-points based sampling method

The DIRECT algorithm was motivated by a modification to Lipschitzian optimization. The algorithm begins its search by sampling the objective function at the midpoint of an interval, where this function attains its lowest value, and then divides this interval by trisecting it. One of its weakness is that if a global minimum lies at the … Read more