Questions tagged [karush-kuhn-tucker]

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions are first order necessary conditions for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.

417 questions
Filter by
Sorted by
Tagged with
42 views

Sufficient conditions for non-convex constrained optimization (KKT)

I am trying to solve an inequality-constrained minimization problem. My objective and constraints are infinitely differentiable but not necessarily convex. I found exactly 1 point $\mathbf{x}^{*}$ ...
16 views

Stationarity condition for non-convex functions

Suppose I have an objective function $$\min_{\bf x} f({\bf x}) + \lambda \|{\bf x}\|_1$$ where $f({\bf x})$ is a differentiable non-convex function. I am trying to derive an upper bound for $\lambda$...
45 views

33 views

48 views

Constrained maximization problem with linear function

I have the following problem. Given this function $E[\pi] = (1-r)[\alpha b- (1-p)C-K]+T$ I would like to find the maximum w.r.t. $r$ given this constraint: $U = (1-r)b-T \geq 0$. It is an economic ...
99 views

Non-linear optimization problem using Lagrange's method/K.K.T. conditions

We are given the following problem: $$\text{minimize } 2x_1^2 + x_2^2 + 3x_3^2 \text{ subject to } x_1+x_2+x_3=10, x_1\le5, \text{ and } x_1,x_2,x_3\ge0$$ I understand that I have to check all ...
37 views

what's the condition of the complex convex problem?

In most books or papers, the convex problems are usually defined on the Real field. However, there are also a lot of works focus on the problem defined on the Complex field but also use the KKT ...
17 views

Convex NLP problem with inequality constraints: is convexity enough to say that points that solve KKT conditions are globally optimal?

Let’s say that we have an NLP problem with inequalities, and we solve the KKT conditions and then find several points that satisfies the KKT conditions. It seems like if the problem is convex and both ...
65 views

63 views

Orthogonal projection into a sparse subspace with $s$ dimension

Traditional orthogonal projection of a given point $y \in \mathbb{R}^n$ into a closed and convex set $D\in \mathbb{R}^n$ is defined as the follwing: $$P_D(y)=\arg\min_{x \in D}||x-y||_2^2$$ Now ...
55 views

32 views

How to solve the KKT condition directly?

According to my understanding, consider a convex optimization problem where the strong duality hold $$\min f(x)$$ $$\text{s.t.}\quad g(x) \leq 0,$$ if a point $x^*$ satisfies its KKT condition,  \...
How could the following problem be tackled? Find the curve $v$ between two points $v(0)=p \neq q=v(1)$ with minimum velocity and acceleration (in the $L^\infty$ sense), such that $v'(0)=v'(1)=0$ I ...