# Tagged Questions

21 views

### Above what order of magnitude a pure cutting-plane algorithm must be forgotten in favour of branch-and-cut?

Crawling the web on the subject of the cutting-plane algorithm, I have seen everywhere that a pure cutting-plane method cannot be used for numerical instability reasons after some iterations. But do ...
21 views

### Can Gomory's cutting plane be used to solve Mixed Integer Linear Programs?

Do you know if Gomory's cut can be used to solve MILP problems ? I have read that Gomory's cut is useful when all variables are integer, but what if just some of them are integer ? Is is necessary ...
66 views

### Forbidden range for a linear programming variable

I would like to express a linear program having a variable that can only be greater or equal than a constant $c$ or equal to $0$. The range $]0; c[$ being unallowed. Do you know a way to express this ...
58 views

### Linearization of a product of two decision variables

I am trying to solve a problem that involves constraints in which products of two decision variables appear. So far, I read that such products can be reformulated to a difference of two quadratic ...
36 views

### How to reformulate this Set covering problem?

I am trying to solve the following implementation of the set covering problem of a crew rostering problem. Here constraint (19), meant to create a 12-hour break between the different shifts taken by ...
37 views

### Linearization of multiple normal functions

I have noticed that it takes a very long time to perform non-linear least squares fitting on datasets similar to this: where there are multiple Gaussian distributions to be fit to experimental ...
77 views

### First-order necessary condition for relative minimum point

I'm studying linear and nonlinear programming and I came across with the following proposition : given $\rm x\in\Omega$ we are motivated to say that a vector $\mathbf d$ is a feasible direction at ...
258 views

### How to linearize the product of two continuous variables in linear programming

I have a question when I deal with a linear programming model. The situation is that: I have some constraints in the model. All the constraints are linear, except some terms, which is the product of ...
52 views

### Some problems with a proof of the Farkas Lemma

The following is a proof of the Farkas Lemma that is creating me quite some problems. [I presented the all proof simply to point out the notation used by the author.] My problem is with the last part ...
22 views

### How to check if steepest gradient method will converge?

So I have this function $f(x,y) = x^4 - 2x^2 +x + 4y^2$ and I want to know if the steepest gradient method will converge if I pick an arbitrary point and apply said method. My initial thought ...
49 views

### Fitting a sine using linear regression

If I have two functions $s_1 = A_1 \sin(\theta+\phi)$ and $s_2 = A_2 \cos(\theta+\phi)$ is it possible to fit a sine or a cosine using linear regression? I usually have much less that a period ...
350 views

### Taylor's theorem for vector valued functions

I'm reading about linear and nonlinear programming and on one page I have the following statment (I have highlighted the areas where I have problems and drawn questions for them in the bottom of it): ...
51 views

### Help to understand the setting up of this Lagrangian

So..I understand up to step 4..but then there are these things I dont get, to start with , it says on (5) that the utility function depended only on the ratios p1/w p2/w ?? why does it say that? ...
37 views

### Regression/compressive sensing with non-linear constrains where the coefficients are assumed to be integer or binary {0,1}

The following regression problem $$\mathbf{y} = \mathbf{A}\mathbf{x}$$ where $\mathbf{y}$ is a $N\times 1$ column real vector, $\mathbf{A}$ is a $N\times M$ real matrix where each column ...
33 views

### Calculating second derivative of $g(\alpha) = f(\textbf{y}(\alpha))$

I'm having problems with the second derivative of the function $g(\alpha) = f(\textbf{y}(\alpha))$ (which I will define more precisely below). I tried calculating it myself, could anyone just simply ...
36 views

### On solving non-linear programming problem and the relevant software

I have a non-linear programming problem, in which all the inequality is linear and only the optimization goal is in a non-linear form. The problem is as following. $x_j$ is the variables and $a_{k,j}$ ...
44 views

### Formulating square packing as a form of optimization

I was looking at square packing problem which is defined as: Given a number N... Find the smallest square that can pack N unit squares Each square can be associated with a 3 dimensional point ...
106 views

### Is this linear programming?

I have the following problem and I'd like to know if it is formalizable as a LP program. (or, more generally, if it is solvable in polynomial time). Let us fix some terminology first which will ...
44 views

### Smooth Reformulation of NonSmooth Constraints

If I have something like : \begin{align} \min_x \max_i f_i(x) \end{align} I can reformulate this nonsmooth formulation as: $$\min_x z$$ $$z\geq f_i(x)$$ and I have a smooth formulation of the problem. ...
182 views

### Is it possible to linearize the non-linear equation in this linear programming?

Have typed the question is latex format, here it is:
99 views

### Solving an optimization problem involving reciprocals

I am trying to solve the following minimization problem, perhaps by getting it into a LP form: Let $u= [u_1, u_2, ...u_N]^T$ a column vector, and $v=[{1\over u_1}, {1 \over u_2}, ...{1 \over u_N}]^T$ ...
446 views

### LP relaxation for ILP\IP (integer linear programming)

I am familiar with LP relaxation for ILP (or IP). Assume we concern with integer minimization problem, which we formalize using ILP; we then relax the ILP into LP and we say that the LP provides a ...
I have to minimize the function: $F(x)$ $F(x) = \sum_{i=1}^{M}||x_{i+1} - x_i - K(\frac{x_{i+1} + x_i}{2})||^2 + ||x_1-c_1||^2 + ||x_N-c_2||^2$ , where $x$ is a vector of $N$ scalars, $c$ are ...