For nonconvex optimization problems, possibly having mixed-integer variables, a convergent primal-dual solution algorithm is proposed. The approach applies a proximal bundle method to certain augmented Lagrangian dual that arises in the context of the so-called generalized augmented Lagrangians. We recast these Lagrangians into the framework of a classical Lagrangian by means of a special reformulation of the original problem. Thanks to this insight, the methodology yields zero duality gap. Lagrangian subproblems can be solved inexactly without hindering the primal-dual convergence properties of the algorithm. Primal convergence is ensured even when the dual solution set is empty. The interest of the new method is assessed on several problems, including unit-commitment, that arise in energy optimization. These problems are solved to optimality by solving separable Lagrangian subproblems.

对于可能具有混合整数变量的非凸优化问题，提出了一种收敛原对偶解算法。该方法将近端丛方法应用于在所谓的广义增广拉格朗日量的上下文中出现的某些增广拉格朗日对偶。我们通过对原始问题的特殊重新表述，将这些拉格朗日函数重铸为经典拉格朗日函数的框架。由于这种洞察力，该方法产生了零二元性差距。拉格朗日子问题可以不精确地求解而不妨碍算法的原始对偶收敛特性。即使对偶解集为空，也能确保原始收敛。新方法的兴趣是在能源优化中出现的几个问题上进行评估的，包括单位承诺。