This paper presents a method for solving a class of constrained optimization problems in finite-dimensional spaces. This type of problem usually arises in connection with parameter optimization in engineering design. Most often, these problems consist of incorporating upper and/or lower bounds on the variables in otherwise unconstrained optimization problems. The proposed method replaces the original optimization problem withm constraints (m>1) by a sequence of optimization problems with one constraint only. The theory behind this method is discussed in the subsequent sections.