Efficient and Adaptive Lagrange-Multiplier Methods for Nonlinear Continuous Global Optimization

摘要: Lagrangian methods are popular in solving continuous constrained optimization problems. In this paper, we address three important issues applying to solve problems with inequality constraints. First, study transform constraints into equality constraints. An existing method, called the slack-variable adds a slack variable each constraint order it an constraint. Its disadvantage is that when search trajectory inside feasible region, some satisfied may still pose effect on function, leading possible oscillations and divergence local minimum lies boundary of region. To overcome problem, propose MaxQ method carries no Hence, minimizing function region always leads objective function. We also strategies speed up its convergence. Second, improve convergence without affecting solution quality. This done by adaptive-control strategy dynamically adjusts relative weights between part, better balance two faster convergence. Third, trace-based pull from one saddle point another fashion restarts. overcomes converges only requires random restarts look for new points, often missing good points vicinity already found. Finally, describe prototype Novel (Nonlinear Optimization via External Lead) implements our proposed present improved solutions collection benchmarks.