  This paper proposes an almost feasible Sequential Linear Programming (afSLP)
algorithm. In the first part, the practical limitations of previously proposed
Feasible Sequential Linear Programming (FSLP) methods are discussed along with
illustrative examples. Then, we present a generalization of FSLP based on a
tolerance-tube method that addresses the shortcomings of FSLP. The proposed
algorithm afSLP consists of two phases. Phase I starts from random infeasible
points and iterates towards a relaxation of the feasible set. Once the
tolerance-tube around the feasible set is reached, phase II is started and all
future iterates are kept within the tolerance-tube. The novel method includes
enhancements to the originally proposed tolerance-tube method that are
necessary for global convergence. afSLP is shown to outperform FSLP and the
state-of-the-art solver IPOPT on a SCARA robot optimization problem.
