Globally tight bounds for almost differentiable functions over polytopes with application to tolerance analysis

It is well known that many decisions can be formulated as optimization problems. This paper presents a simple alternative approach to solving linearly constrained global optimization problems with almost differentiable objective functions. The unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region. The proposed algorithm has the following features: it is a general-purpose algorithm; i.e., it employs one common treatment for all cases; it guarantees global optimization in each case, unlike other general-purpose, local optimization algorithms; it has simplicity because it is intuitive and requires only first order derivative (gradient); and it provides useful information for sensitivity analysis. The algorithm and its applications to tolerance analysis are presented in the context of numerical problems.