| 1. | Augmented lagrangian function and approximate optimal solutions in nonlinear programming
非线性规划中的增广拉格朗日函数与近似最优解 |
| 2. | When adding an entropy function as regularizing term to the lagrangian function , we obtain a smooth approximate function for m ( x ) , which turns out to be the exponential penalty function
当将熵函数作为正则项加到拉格朗日函数上，我们得到了逐点逼近于m ( x )的光滑函数。经证明，该函数即为指数罚函数。 |
| 3. | The objective function of the qp problem is a quadratic function which is an approximation of the lagrangian function of the constrained problem and the constraints of the qp problem are linear approximation of the constraints of the constrained problem
这些二次规划子问题的目标函数是原约束最优化问题的lagrange函数的二次某种近似，其约束条件是原约束最优化问题的线性逼近。 |
| 4. | Maximum entropy method is an effective smoothing one for the finite min - max problem , which , by adding shannon ' s informational entropy as a regularizing term to the lagrangian function of min - max problem , yields a smooth function that uniformly approaches the non - smooth max - valued function
极大熵方法是解有限极大极小问题的一种有效光滑化法，它通过在极大极小问题的拉格朗日函数上引进shannon信息熵作正则项，给出一致逼近极大值函数的光滑函数。 |
| 5. | To circumvent the non - differentiable difficulty caused by the positive homogeneously function that is involved in an equivalent unconstrained formulation for general inequality constrained optimization problems , we turn to the classical lagrangian function and redefine m ( x ) by a conic optimization problem with the lagrangian as the objective function
为了克服不可微正齐次函数( ? | r _ - ~ m )给约束优化问题的等价无约束形式求解带来的困难，我们将其目标函数m ( x )重新用一个以经典拉格朗日函数为目标的锥优化问题来表示。 |
| 6. | In latter part of chapter three , some exciting properties of the revised lagrangian function discussed first , which leads to form a dual algorithm of cora or cot . convergence theorem proved by banach perturbation theorem , bertsekas implicit function theorem ii and by analyzing hesse matrix of revised largrangian function
另一类是构造相应的lagrange函数及其一种对偶算法的迭代格式，讨论了修正lagrange函数的性质，并借助banach扰动定理及bertsekas第h隐函数定理，及对修正lagrange函数hesse阵分析，证明了该算法的收敛性 |
