Intuitive Mathematical Economics Series. Constrained Maximization and the Method of Lagrange Multipliers
نویسندگان
چکیده
منابع مشابه
On the Method of Lagrange Multipliers
and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...
متن کاملLagrange Multipliers and Optimality
Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...
متن کاملLagrange Multipliers with Optimal Sensitivity Properties in Constrained Optimization
We consider optimization problems with inequality and abstract set constraints, and we derive sensitivity properties of Lagrange multipliers under very weak conditions. In particular, we do not assume uniqueness of a Lagrange multiplier or continuity of the perturbation function. We show that the Lagrange multiplier of minimum norm defines the optimal rate of improvement of the cost per unit co...
متن کاملLocal Stability Conditions for the Babuska Method of Lagrange Multipliers
We consider the so-called Babuska method of finite elements with Lagrange multipliers for numerically solving the problem Au = f in il, u = g on 3Í2, iî C Rn, 7i > 2. We state a number of local conditions from which we prove the uniform stability of the Lagrange multiplier method in terms of a weighted, mesh-dependent norm. The stability conditions given weaken the conditions known so far and a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2018
ISSN: 1556-5068
DOI: 10.2139/ssrn.3333448