Handling inequality constraints in continuous nonlinear global optimization
Tao Wang, Benjamin Wan-Sang Wah · 1996
In this paper, we present a new method to handle inequality constraints and apply it in NOVEL (Nonlinear Optimization via External Lead), a system we have developed for solving constrained continuous nonlinear optimization problems. In general, in applying Lagrange-multiplier methods to solve these problems, inequality constraints are first converted into equivalent equality constraints. One such conversion method adds a slack variable to each inequality constraint in order to convert it into an equality constraint. The disadvantage of this conversion is that when the search is inside a feasible region, some satisfied constraints may still pose a non-zero weight in the Lagrangian function, leading to possible oscillations and divergence when a local optimum lies on the boundary of a feasible region. We propose a new conversion method called the MaxQ method such that all satisfied constraints in a feasible region always carry zero weight in the Lagrange function; hence, minimizing the L...