The Lagrangian, constraint qualifications and economics
نویسندگان
چکیده
Abstract Considering constrained choice, practitioners and theorists frequently invoke a Lagrangian to generate optimality conditions. Regular use of that vehicle requires, however, some constraint qualification . Yet many economists go easy on the mathematics issue. Conversely, few mathematicians elaborate economics context. Thereby both parties leave lacunas as didactics or intuition. This note attempts shed light these matters.
منابع مشابه
Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are consequence of the constrained syst...
متن کاملConstraint Qualifications for Nonlinear Programming
This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...
متن کاملThe Lagrangian Relaxation Method for the Shortest Path Problem Considering Transportation Plans and Budgetary Constraint
In this paper, a constrained shortest path problem (CSP) in a network is investigated, in which some special plans for each link with corresponding pre-determined costs as well as reduction values in the link travel time are considered. The purpose is to find a path and selecting the best plans on its links, to improve the travel time as most as possible, while the costs of conducting plans do ...
متن کاملTwo New Weak Constraint Qualifications and Applications
We present two new constraint qualifications (CQ) that are weaker than the recently introduced Relaxed Constant Positive Linear Dependence (RCPLD) constraint qualification. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had...
متن کاملGeometry of optimality conditions and constraint qualifications: The convex case
The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the "badly behaved set" of constraints, i.e. the set of constraints which causes problems in the Kuhn-Tucker theory, is isolated and a computational procedure for checking whether 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: Mathematical Methods of Operations Research
سال: 2022
ISSN: ['0042-0573', '1432-5217', '1432-2994']
DOI: https://doi.org/10.1007/s00186-022-00789-7