Questions tagged [quadratic-programming]
For questions on quadratic programming, methods to solve them and related solvers. Use this tag along with (optimization).
29
questions with no upvoted or accepted answers
8
votes
0
answers
112
views
For subset selection regression as a mixed integer program, how tightly should the bounding box be set?
When solving best subset regression as a mixed integer program, how do you decide how tightly to bound the range of values of the $X$ values? When the box is tight, the solver finds a solution ...
- 261
6
votes
0
answers
126
views
Water quality component optimization
I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
- 61
6
votes
0
answers
138
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 ...
- 3,980
4
votes
0
answers
169
views
Analytical solution of constrained quadratic program
I'm trying to solve a "simple" (= small) optimization problem often, with only minor changes to the objective function. Therefore it's important to keep the "time per solve" as low ...
- 41
3
votes
0
answers
124
views
Continuous optimization with a Euclidean TSP objective
I am trying to solve a problem of the form $$\min_{x_1,\dots,x_n} f(x_1,\dots,x_n)$$ subject to a constraint that $\mathrm{length}(\mathrm{TSP}(x_1,\dots,x_n))\leq c$, where $x_1,\dots,x_n$ are all ...
- 149
3
votes
0
answers
119
views
From Quadratic to MILP?
I am playing around with some Quadratic Programs (QPs), and I want to check if my reasoning is right concerning a re-modeling from QP to MILP. So, let's consider the below QP:
(QP) $\min c^T x + x^T Q ...
- 1,238
3
votes
0
answers
136
views
Linearize objective function with non-linear terms
I have a problem with linear constraints but in the objective function I want to have some linear terms along with a $x^2$ term. So it is like the following:
$$\min \sum \limits _i \sum \limits _j (a[...
3
votes
0
answers
100
views
Automatic quadratization of constraints in pyomo for gurobi
Gurobi 9 can solve QCQPs, and QCQPs capture all of polynomial optimization by the obvious trick that e.g. a cubic term $x_1 x_2 x_3$ can be turned into a quadratic term $y x_3$ and a constraint $y = ...
3
votes
0
answers
150
views
SDP relaxation with greater-than and less-than inequalities at the same time
I am dealing with the following nonconvex fractional quadratic optimization problem
\begin{align}
& \min_{\boldsymbol{x}} && \max_{t \in \mathcal{T}} \frac{\boldsymbol{a}_t^T \boldsymbol{...
2
votes
0
answers
81
views
Does the value function of a quadratic program stay convex when adding constraints?
I am interested in the value function of a quadratic program of the form
$$
v(y)=\min_x \frac{1}{2} x^\top Q(y) x,
$$
subject to a linear equality constraint
$$
E(y)x=d(y),
$$
and a linear inequality ...
- 121
2
votes
0
answers
111
views
Is this semidefinite constraint in fact pointless?
On Wikipedia, I encountered a statement that the semidefinite relaxation of a quadratically constrained quadratic program can be solved more efficiently (using only LP) in the case that no variable is ...
- 201
2
votes
0
answers
153
views
How to linearize this multiplicative constraint?
I have a constraint in the form
$\sqrt{|\sum_{c\in C}{h_cw_c}|^2}\ge\sqrt{x}\zeta$
Here, $h_c$ is s row vector (know), $w_c$ is a column vector (variable).
$x$ and $\zeta$ are also optimization ...
- 2,265
2
votes
0
answers
67
views
Determine set of "arbitrage-free" regional prices
I am seeking for a way how to determine set of "arbitrage-free" regional prices for a single commodity market.
There are $N>1$ production units with costs $C^{prod}_i, i=1,\dots,N$ and ...
- 21
2
votes
0
answers
123
views
Indicator function for integer variable with inequality constraint
I have $n$ integer variables $\vec{x}$ with the following integer programming problem.
$$
COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0)
$$
Here, $a_i, b_j \in \mathbb{R}_+$ ...
- 251
2
votes
1
answer
406
views
MIQP — CVXPY unable to treat summation of variables as a variable
I have a quadratic integer programming assignment problem. The goal is to assign riders seats on a bus such that distance between any two riders is maximized; however, the importance of each objective ...
- 551
1
vote
0
answers
60
views
Quadratic conic program duality
I am working on a problem relating to what is known as the "Good Deal risk measure" for production valuation in incomplete markets. I have created the following primal optimization problem, ...
1
vote
0
answers
37
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}$ ...
- 3,980
1
vote
0
answers
74
views
Does Gurobi solve QCQMIPs with Quadratic terms faster with then Bi-Linear terms in general?
Based on the color distance function defined here i try to find $n$ RGB colors with large inter set color distances and good color distance to white.
...
- 4,007
1
vote
0
answers
67
views
Dual of a quadratic constraint
This is my model.
\begin{align}
\min_x&\quad\sum_{e\in E} X_e p_e \\
\text{s.t.}&\quad\sum_{e \in E: T(e)=i} X_e - \sum_{e \in E: H(e)=i} X_e = \begin{cases}1, \;\text{if}\;i=s\\-1,\;\text{if}...
- 517
1
vote
0
answers
174
views
Optimization Multiple Constraints
I am trying to solve a linear algebra problem: an optimization problem and I am using CVXOPT. I've split the problem into 3 components
In its simplest form, The general formulation for CVXOPT is \...
- 173
1
vote
0
answers
264
views
Solver issue? Xpress (slp) - Nonlinear - Python - Pyomo
I tried solving my model with xpress:
pip install xpress
And then in the model:
...
- 111
1
vote
0
answers
93
views
Question on quadratically constrained quadratic program
If the constrained optimization problem is a quadratically constrained quadratic program of the form \begin{align}\min&\quad x^HQx-a(x+x^H)+b|z^Hx|^2\\\text{s.t.}&\quad\|x\|^2\le1\end{align} ...
- 19
0
votes
0
answers
58
views
Is it possible to transform MIQP into MILP without introducing new variable?
I have a QP optimization problem in the form
$$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$
here $\bf Q$ is a symmetric matrix.
$\bf x$ is the optimization variable, and it is binary.
Is there a way to ...
- 2,265
0
votes
0
answers
34
views
Projection of QP problem solved with Gradient Descent
Lets say we have a QP problem as shown below
$$\min {\bf x}^T {\bf R}{\bf x}+{\bf c}^T{\bf x}$$
subject to
$${\bf A_{eq}x}={\bf e}_{eq}$$
$${\bf Ax}\le {\bf e}$$
$${\bf x}\in \lbrace 0,1\rbrace$$
${\...
- 2,265
0
votes
0
answers
53
views
Better formulation of bilinear terms
I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
- 23
0
votes
0
answers
32
views
Unclear points in derivation of Lagrange duality for a quadratic optimization problem
Problem0:
$\displaystyle \min_{\mathbf{u} \in \mathbf{R}^L}\frac{1}{2}\mathbf{u}^TQ\mathbf{u}+\mathbf{p}^T\mathbf{u}$
$\,$ subject to $\,$ $\mathbf{a}^T\mathbf{u} \ge c$
Problem1:
$\displaystyle \...
- 409
0
votes
0
answers
16
views
Problem in understanding an equation from a paper about iterative Linear-Quadratic Regulator
I'm reading a paper about iterative Linear-Quadratic Regulator (iLQR) and there are a lot of points that I don't understand.
https://homes.cs.washington.edu/~todorov/papers/TassaICRA14.pdf
I think ...
- 101
0
votes
0
answers
62
views
How do I implement this convex problem in CVXPY?
I am looking to implement the following optimization problem in CVXPY.
$$ \max _{x_t} x_t' \mu - \frac{\gamma}{2} x'_t \Sigma x_t - x'_t\Lambda \Delta x_t $$
where $\Delta x_t := x_t - x_{t-1}$ and $\...
- 1
-1
votes
0
answers
63
views
Improving performance of gurobi program
I have $n$ points in an $n$-dimensional space (more specifically, the points are basis vectors with small random perturbations).
I want to embed the points into a smaller-dimensional space: i.e. for $...
- 99