Questions tagged [optimization]

Mathematical techniques for the selection of a best element (with respect to some criteria) from the set of available alternatives.

181 questions
Filter by
Sorted by
Tagged with
2k views

394 views

Karush-Kuhn-Tucker in infinite dimension

Does the Karush-Kuhn-Tucker theorem on sufficient conditions for optimality of a convex program apply in countable dimension? For precisions, see Definition 4.1.1 and Theorem 4.1.4 of this course. ...
951 views

Dynamic Optimization: What if the second order condition does not hold?

Consider the following dynamic optimization problem \begin{align} &\max_u \int^T_0{F(x,u)dt}\\ \text{s.t.}~& \dot{x} = f(x,u) \end{align} FOCs The Hamiltonian is given by \begin{align} H(x,u,...
1k views

Why couldn't the Karush-Kuhn-Tucker optimization find the solution?

I have the following utility maximization problem: $$\max (xy)$$ $$(x+y-2)^2 \leq 0$$ Conditions: $$y-2\lambda (x+y-2) =0$$ $$x-2\lambda (x+y-2) =0$$ $$\lambda(x+y-2)^2=0$$ When I set $\lambda>0$, ...
723 views

Is there a way to link Berge's theorem of maximum to Envelope theorem?

Berge's theorem states Let $X \in \mathbb R^m, \Theta \in \mathbb R^n$, $f : X \times \Theta \to \mathbb R$ be a jointly continuous function, $C : \Theta \rightrightarrows X$ be a continuous(both ...
6k views

Leontief preferences

I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
87 views

Overlaping jurisdictions model, Alesina Spolaore: Proof of Lemma 1; The Size of Nations

I've been reading the book 'The Size of Nations' by Alberto Alesina and Enrico Spolaore (can be found on the net if you know where to look) and I'm having trouble following their "proof" of ...
115 views

Identification of switching costs from price shocks

What, if anything, can we learn about customer switching costs by looking at price, revenue, profit, and quantity responses of producers to cost shocks? For example, we can define the profit equation ...
157 views

Simple Derivation of Maximum Principle

Consider the simplest problem of optimal control \begin{align} &\max_u\int^T_0{F(y,u)dt}\\ \text{s.t.} \quad&\dot y = f(y,u)\\ & y(0) = y_0\\ & y(T)~~\text{free} \end{align} ...
240 views

Optimization: Dynamic Programming vs Kuhn-Tucker

Considering the standard utility maximization of representative household which lives forever, one may use dynamic programming and Kuhn-Tucker in case of discrete time. For instance, one would like to ...
129 views

Mythbusters - Determine optimal boarding strategy based on time and satisfaction score

Most airlines board passengers starting from the back of the plane and then working their way towards the front (after boarding priority classes and passengers). In an episode of Mythbusters, Adam ...
109 views

Applications of Optimal Transport in Economics

The 1975 Nobel Prize winner in Economics was Kantorovich who reformulated the optimal transportation theory of Monge and applied it to optimal resource allocation. The Wasserstein distance is central ...
135 views

GE with an intermediate good

intro I'm looking at a simple model with 1 consumer, 2 goods and 2 firms. I'm trying to get a price vector [p0, p1] that makes it work. By makes it work, I mean, ...
256 views

Optimization of Households' utility in “ Rule-of-Thumb Consumers and the Design of Interest Rate Rules ” (Gali et al., 2004)

I can't figure out how the calculation of first order conditions was carried out. I can't figure out where the stochastic discount factor came from.
804 views

Examples of non-differentiable problems in economics

As a research project, we're investigating various algorithms developed for non-differentiable, convex (or concave, if you're into economics) optimization. I'd like to find some good examples of real ...
600 views

Kuhn Tucker Conditions with fewer non-negativity constraints than number of variables

I have a following type of problem: $Maximize\,\, F(s,x,y,z)$ $s,x,y,z$ s.t. (i) $g(x,y,z) \le I$ (ii) $x \ge 0$ (iii) $y \ge 0$ (iv) $s > 0$ That is there is no non negativity constraint on ...
77 views

When can one drop time subscripts? Example from Angrist and Kugler (2003)

Not the first time I am asking myself, but in this paper they actually start with a time dependent maximisation problem and then drop all time subscripts. Background: They have profit maximisation ...
237 views

Arrow-Debreu Theorem of Existence: Non satiation

Let $n$ be the number of consumers and $m$ be the number of commodities. The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
326 views

Estimating the second derivative of function from optimizers

Consider the following optimization $$x^*(s) = \max_{x\in X} \big(\,f(x)-sx\,\big)$$ where $f$ is assumed to be a strictly concave function and $X$ is an interval constraint, e.g $X = [0,b]$. We do ...
1k views

Does the Marshallian demand function always include prices and income?

I have the following utility function: $$U(x_i)=x_1x_2+x_3$$ with budget constraint: $$p_1x_1+p_2x_2+p_3x_3\leq I$$ I use the Kuhn-Tucker method to find the optimal choices of the Utility ...
101 views

317 views