Many situations ranging from industrial to social via economic and environmental problems may be cast into a Semi-infinite mathematical program. In this paper, the cutting-plane approach which lends itself better for standard non-linear programs is exploited with good reasons for grappling with linear, convex and geometric Semi-infinite programs. For each case, computational aspects are discussed and convergence statements established. Simple numerical examples are also provided for the sake of illustration. The paper ends by briefly comparing the cutting-plane approach
discussed here with other existing approaches and by stressing the necessity of pushing forward a Decision Support System effectively capable for helping someone faced with a problem that can be formulated as a Semi-infinite mathematical program.