New Lagrange multiplier method

Inequality constraints were handled with the similar method as their equality counterparts in Lagrange multiplier method, while the multipliers associated with inequality constraints were written as a positive definite function of the originally-defined multipliers. Based on this, a new Lagrange multiplier method is proposed and its convergence rigorously analyzed. The underlying mechanism that leads to the algorithmic convergence is uncovered, and some measures for relaxing the convergence conditions and enlarging the attractive domain are discussed by the LaSalle invariance principle. The result showed that the algorithm attained optimal solution both by stable and unstable factors.