| This dissertation relates theoretical and computational techniques to solve nonlinear and nonsmooth optimization problems. The theoretical work shows different relationships among the nonsmooth concepts: interval slopes, generalized gradients, semigradients and slant derivatives. Theorems are proven to provide these relationships.; Twin arithmetic is incorporated to implement an automatic twin slope computation, which provides simultaneously inner and outer bounds for the range and the slope set of a real function in a given interval.; Verified solutions of nonlinear and nonsmooth optimization problems are done with rigorous computations of the objective function and slope intervals, which are based in nonsmooth interval concepts. |
