# Questions tagged [reformulation-linearization]

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### Maximizing a Ratio/Percent

I'm using cvxpy to model a problem. Inside a very large and complex LP, I create two continuous, affine (unconstrained) expressions: $x$ and $y$. Due to how they ...
• 195
220 views

### How to treat a system of bilinear constraints

A model contains constraints of the following form $R(k) \leq X(k) G(k)$ where $X(k)$ binary and $G(k)$, $R(k)$ non-negative variables. The index $k$ runs from $1$ to $50$. I linearise the equations ...
• 2,252
145 views

### Cases where RLT/SDP relaxation does not work well with standard quadratic optimization

(For people who don't know what RLT is): I am maximizing an indefinite quadratic function over a standard simplex, i.e., the standard quadratic optimization problem. A well-known approach is to relax ...
• 4,010
445 views

### Can we linearize the division of a binary variable by a continuous variable?

I'm trying to solve an MINLP problem where the following division term is appearing in the objective: $$z_r = \frac{x_{ry}}{\sum_r d_r x_{ry}}, \forall r, y,$$ where $x_{ry}$ is a 2D binary variable ...
348 views

### Piecewise linear and global optimization

I am new to OR, and apologies if my mathematical notation is not clear. I have tried my best to keep it concise and given an explanation with numerical data. I would like to understand: Can this ...
• 81
278 views

### How to deal with an optimization problem that have a sum of nonlinear functions of Z as a constraint when Z is the quantity to be minimized?

I have to minimize a quantity $Z$ subject to the following constraints: $$w_1 + w_2 + w_3 = 1 \tag{1}$$ $$\frac{f_1(w_1 Z) + f_2(w_2 Z) + f_3(w_3 Z)}{Z} \ge k \tag{2}$$ where $k$ is a known ...
• 141
293 views

### Switching of decision variables to be equal to a certain decision variable according to a binary (indicator) variable

I would like to seek some advice on modeling the following: I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third ...
• 741
166 views

### DCP formulation of sum of nonconvex and convex functions

I am trying to find a DCP formulation for the following convex objective function (using CVXPY): Let $x$ be the $N$-dimensional vector variable on which we optimize on, $c$ be a known scalar value ...
• 41
151 views

### How to reformulate the BigM constraints into its equivalent Convex-hull formulation?

I am trying to work on a scheduling problem based on its polyhedron reformulations. For that, I would like to reformulate a BigM model into its equivalent C-hull formulation. The transforming map is ...
• 9,133
191 views

1 vote
71 views

### On Linear Relaxation of Standard Quadratic Programming

Consider the following StQO problem where matrix $Q$ is indefinite: \begin{align*} \text{minimize} \quad & x^\top Qx \\ \text{subject to} \quad & e^\top x = 1, \\ & ...
1 vote
137 views

### How to avoid division by zero with a binary variable at the denominator in a network assignment problem?

I am currently working with some network assignment problem as a network engineer. My engineering application can be stated as follows: There are $M$ users that needs to be assign to $N$ servers. This ...
1 vote
45 views

### Converting a function composing of multipe pieces into a linear equation

I have a variable (alpha) which depends on some other binary variables, denoted as X_i. So, for some combination of other variables, alpha may take a value (Beta_j). I added some auxillary variables (...
• 97
1 vote
44 views

### How to force a bounded relationship to "become redundant" or "not needed"?

As an engineer who is currently working with some optimization problem I am currently running into a difficult reformulation problem. Here $a$ is a binary decision variable, $\phi \in [0,1]$ and $d$ ...
1 vote
39 views

### Convex quadratic maximization over cartesian product of simplices

Suppose we are maximizing $f(x^1,\ldots,x^t)= \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}^\top Q \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}$ ...
• 4,010
84 views

### Min-convex function as constraint

I have a constraint that is as follows: $$Ax - f(x) \leq 0$$ where $f(x)=min_y(g(x,y))$. Which is convex. I can even get the gradient in $x$. How can I reformulate my constraint? or what ...
• 517
Consider the following QP problem, where the matrix $Q$ is positive definite: \begin{align*} \max_{x} \quad & x^\top Qx + c^\top x \\ \text{s.t.} \quad & Ax \geq b, \\ & ...