# Tagged Questions

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 ...

41 views

12 views

13 views

### Indefinite Boolean Quadratic Programming: number of minima

The Boolean Quadratic Programming problem is defined as: $\min_{x} f(x) = x^TQx + c^Tx$ s.t. $x \in \{0,1\}^n$ It is a well-studied NP-Hard problem with many approximation algorithms proposed. I ...
20 views

### Solving optimization problem where objective function is of type (affine+(affine/affine))

I need to solve a non linear optimization of the form minimize $f(x) +\frac{g(x)}{h(x)}$ subject to $p(x)\leq0$ $q(x)=0$ Here $f,g,h,p,q$ are affine functions of $x$ and they are convex in the ...
51 views

### Knapsack or bin packing problem?

I have $i$ items and I should pre-packed $m$ knapsacks with identical items where only $K<n$ items can be packed. Also, we should have only one of each item in each sack. The time capacity for ...
29 views

### Is this Feasibility problem NP-hard?

I am trying to solve a combinatorial optimization problem (a feasibility problem) and I have very little idea of solving such problems. The problem is as follows: Solve for $\phi$; \...
11 views

### Estimate parameters in min function $U(a,b)$ = $min[(b-x_i)^2,(a-x_i)^2]$

I have got a list os measures and I need to estimate 2 sizes for this measures. I have the following function that estimates this 2 sizes. $U(a,b)$ = $min[(b-x_i)^2,(a-x_i)^2]$ being $a$ the first ...
26 views

11 views

### Creating gradient functions based on model parameters?

I am using a software library (Math.Net) to try to fit two Lorentzians to a curve. I have found some example software which shows the fitting out a few various types of curves (Line, Parabola, Power ...
40 views

18 views

69 views

### Finding the maximum area of a triangle with a perimeter constrain

Using graphical methods, determine the dimensions of a right triangle that has the largest possible area, given that the perimeter cannot be larger than $P$. The final answer should be in terms of $P$....
28 views

### How to find matrix $A$ from the relation: $A\times (A^TA)^{-1}\times A^T = B$

Kindly help me in the following: I have two Matrices, $A$ of size $(n\times m)$; and $B$ of size $(n\times n)$, where $n>m$. $A$ is unknown, but $B$ is known. $(A^TA)$ is invertible $B$ is ...
25 views

### show that $\Big(\sum_{i=1}^{n}\alpha_i ^2\Big)^2\leq\Big(\sum_{i=1}^{n}\alpha_i \Big)\Big(\sum_{i=1}^{n}\alpha_i ^3\Big)$

Let $\alpha_1,\alpha_2,...,\alpha_n>0.$ How can I show that $$\Big(\sum_{i=1}^{n}\alpha_i ^2\Big)^2\leq\Big(\sum_{i=1}^{n}\alpha_i \Big)\Big(\sum_{i=1}^{n}\alpha_i ^3\Big).$$ Please provide me ...
15 views

### Approximating a quadratic term in the constraint set as 2nd order Taylor expansion

I have an optimization problem in the following form: $$\min_{x,y} f(x)+g(y)$$ $$s.t.$$ $$Ax+h(y)=0$$ where $h(y)$ is a quadratic in $y$. Instead of solving this problem directly, $h(y)$ is ...
21 views

10 views

### Nonlinear regression output in R

Suppose one is interested in doing a nonlinear curve fitting procedure such as $Y=AX^B$ where $a,b \in \mathbb{R}$. If the regression were linear, one usually observes the standard error of the ...
22 views

### Optimisation Problem [closed]

Given a vector $\vec{c}$ and a radius $r$, solve the problem: \begin{equation*} \begin{aligned} & \underset{x}{\text{maximise}} & & \vec{c} \cdotp \vec{x}=a \\ & \text{subject to} &...
22 views

### $L^p$-norm minimization under linear constraints: Does the optimum depend on $p$?

Consider the following norm minimization program: \begin{align} \label{1} &\min_{x \in \mathbb{R}^d} &&\lVert x - x_0 \rVert_p^p &(1)\\ &\text{subject to } &&Ax-b \ge 0 \...
36 views

### Rosenbrock function matlab

I am new to MATLAB and I am asked to implement on matlab the following algorithm: for an unconstrained minimisation problem. I am asked to apply the BFGS method with armijo line search (backtracking)....
52 views

12 views

### How to optimize a non-convex function with nonlinear equality constraints

$$\min \|X-UV\|$$ $$\textbf{s.t.} \|Uz_i\|_{2}=1$$ with $V_{n\times m}=(z_1,z_2,...,z_m), z_i=(v_{i1},v_{i2},...,v_{in})^{\top}$
27 views

27 views

12 views

### Which are the alternative approaches to stochastic (online) gradient descend for online optimization?

I'm looking for some alternative approaches to online\stochastic gradient descent for online optimization such that 1) there exists some proof about the convergence of the parameters to some compact ...
22 views

### Can the constrained optimization problem (1) be transformed into the unconstrained form (2)

(1) \label{constrained} \begin{array}{cl} \arg \min \limits_{\mathcal{C}_k} & \text{rank}(\mathcal{C}_k)\\ \mathrm{s.t.} & \mathcal{E}(\phi_{j}^{k})\le \epsilon \end{...
26 views

### Are the constrained optimization problem equal to the unconstrained one?

(1) $$\label{constrained} \begin{array}{cl} \arg \min \limits_{x} & \|Ax-b\|_2\\ \mathrm{s.t.} & \|x\|_1\le \epsilon \end{array}$$ (2) \label{...
31 views

### Why the trace norm of a tensor is a good approximation to its rank?

In many literature, they use the trace norm of a tensor to approximate its rank, which is defined as follows: $$\|\mathcal{X}\|_{\ast}:=\sum_{i=1}^{n}\alpha_i\|X_{(i)}\|_{\ast}$$ where ${\alpha_i}'s$ ...
Gauss-Newton algorithm How would I go about proving this? For the problem $$min \ f(x) = \frac{1}{2} \Sigma_{j=1}^m r_j(x)^2$$ The equations for the search direction $$J_k^TJ_kp_k=-J_k^Tr_k$$ ...
How does one go about proving non-convexity of the function d? $$d(v) = 1/2*||F(v)- p||^2$$ $$F(v)=\sum_{i=1}^n l_i*\begin{pmatrix} cos(\sum_{j=1}^i v_j) \\ sin(\sum_{j=1}^i v_j \end{pmatrix}$$ ...