Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [nonlinear-optimization]

A non-linear optimization problem includes an objective function (to be minimized or maximized) and some number of equality and/or inequality constraints where the objective or some of the constraints are non-linear. Use this tag for questions related to the theory of solving such problems or for trying to solve particular problems.

A non-linear optimization problem includes an objective function (to be minimized or maximized) and some number of equality and/or inequality constraints where the objective or some of the constraints are non-linear. Usually, non-linear optimization problems are much harder to solve than linear ones.

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Looking for a solution for the following non linear optimization problem

I've previously solve optimization problems with linear and mixed integer linear programming with Simplex Algorithm. Now I've an objective function $F=f(x_1, x_2, .. x_n)$ to be minimized, but F is not lineare and its value is computed by an…
daniele
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Does a local minimum of a function always satify the Armijo rule

Does a local minimum of a function always satify the Armijo rule?
DogDog
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Showing that $x_{k+2}$ is a point which approximates a maximum?

Suppose that $x_kf'(x_{k+1})$. How can I show that the secant method will give $x_{k+2}$ as a point which approximates a maximum? $$x_{k+2}= x_k-\frac{f'(x_k)(x_{k+1}-x_k)}{f'(x_{k+1})-f'(x_k)}$$
tayyebe
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Zero-order necessary conditions

I have a question regarding the Zero-order necessary conditions. In my Linear and Nonlinear programming book it is stated: Consider the set $\Gamma \subset E^{n+1} = \{(r,\textbf{x}): r\geq f(\textbf{x}), \textbf{x}\in E^n\}.$ In a figure of the…
jjepsuomi
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Implement $\max$ with a closed form expression?

I have 2 functions: $f(x)$ and $g(x)$. Both of them range in $[0,1]$. Is there some way to define a $h(x)$ that efficiently takes the greater one of $h(x)$ and $g(x)$, i.e. $h(x) = \max \{ f(x),g(x) \}$, but without using $\max$? If there is no…
Jokester
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Sets of feasible directions

I'm not exactly sure how the different points matter. I believe $p=[1,1,-1]^T, [2,-1,0]^T, [3,0,-1]^T, [0,3,-2]^T$ are all feasible directions.
user142112
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lagrange multiplier for more than 2 equality constraints

i couldn't do the following question for hours minimize $\sum_{i=1}^{n}x_{i}^{3}$ s.t. $\sum_{i=1}^{n}x_{i}=0$ and $\sum_{i=1}^{n}x_{i}^{2}=n$. by Lagrange multiplier rule ?
nur
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Nonlinear optimization in exponents

$$ max \pi = 4x_1^\frac{1}4x_2^\frac{1}3 - x_1 - x_2 $$ It is not difficult to determine that this function is concave and yields a global maximum at some point for the quantities $ x_1, x_2 >= 0 $ My problem is in identifying the optimal quantities…
Martin Erlic
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Converting Non-linear Programming Problem from Maximization to Minimization

I have a non-linear maximization problem and I want to convert it to be a minimization problem, can I do so by multiplying it by a negative sign, or is that wrong; and if that is wrong what should I do? Thanks a lot
user122289
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Maximum of convex functions

how can i proof that: If $f_1, . . . , f_m$ are convex functions,than function $F(x) = \max(f_1(x), \dots , f_m(x))$ is convex? thanx for help.
user111673
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maximizing a function of a positive semi-definite matrix with bounded trace

I need to maximize a function $f(A)$ where $A$. With the constraints that $A$ is positive definite and has a trace $tr(A) \leq K$. $tr(A)=K$ will work for my problem too. I can differentiate towards $A_{ij}$ and use Lagrange multipliers for the…
user40607
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Gauss-Newton equation with robust function Huber

According to the Gauss-Newton algorithm, it was used to minimize the sum of square loss $f = \dfrac{1}{2}r^2$ where $r$ is the residual and it can be written as $r = y-f(x)$. The normal equation of Gauss-Newton is $J^TJx=-J^Tr$ where $J$ is known to…
Jacob Chang
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Minimize a nonlinear sum subject to a quadratic constraint

Currently I am solving an optimization problem that could be written as follows: $$\min J= \sum_{i=1}^N {(q_i^H\Lambda q_i)}^{\frac{1}{3}} $$ subject to $\{q_i\}_{i\in [1..N]}$ forming an orthonormal basis. $\Lambda$ is a symmetric matrix with size…
The Researcher
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how do i find $\max\{x+z\}$ and $\max\{1+y^2\}$ where ?$x\ge0 $,$ y\ge0$,$ z\ge0$ and$xy+xz+yz=1 $

how compute $\max\{x+z\}$ and $\max\{1+y^2\}$? such that $x$,$y$,$z$ satisfied $$\begin{cases} xy+xz+yz=1 & \\ x\ge0 \\ y\ge0\\ z\ge0\\ \end{cases} $$ i face with this problem when i try solve here Thanks in advance
M.H
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residual temporal decay weights on constrained nonlinear least squares (Python scipy SLSQP)

I have a constrained nonlinear least squares minimisation problem set up (using Python scipy's SLSQP solver) that looks something like: $$\min_w \frac{1}{N}\sum_i (P_i-O_i)^2,$$ where $P=\sum_j w_j p_j, \ \ \ \ $ $p_j$ are prediction probabilities…
vzografos
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