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Questions tagged [quadratic-programming]

For questions on quadratic programming, methods to solve them and related solvers. Use this tag along with (optimization).

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Time complexity of QP solver

Could you suggest any papers or other resources that report the computational time complexity (e.g., O(n^3)) of the OSQP solver for Quadratic Programming (convex optimization), or at least the ...
Enk9456's user avatar
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1 vote
1 answer
88 views

How to do the scaling to remove bias in QP problem?

I have a MIQP problem as below minimize $$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$ ${\bf x}$ is a binary variable. The range of values in ${\bf Q}$ and ${\bf x}$ are quite different. The elements of $...
KGM's user avatar
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2 votes
1 answer
81 views

Is the linearization with first-order Taylor approximation correct?

I have a QP problem as $\min \hspace{2mm} x^TQx-c^Tx$ here $x$ in binary I want to transform it into a MILP by writing the objective function as $\min \hspace{2mm} z-c^Tx$ and then adding a constraint ...
KGM's user avatar
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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 ...
KGM's user avatar
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1 vote
1 answer
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Linearizing a quadratic constraint

I am working on a quadratic conic optimization problem, but I have discovered that it would be preferable if the quadratic constraint is linearly approximated. In other words, I need some way to make ...
Mikkel Honningsvåg Sandhaug's user avatar
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40 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 $${\bf A_{eq}x}={\bf e}_{eq}$$ $${\bf Ax}\le {\bf e}$$ $${\bf x}\in \lbrace 0,1\rbrace$$ ${\...
KGM's user avatar
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1 answer
87 views

How to model this constraint for a QP problem?

I have a system with 100 users. There are 6 resources. At any point of time, only 2 resources are made available and those resources can be shared among the users. Some users may not get any resource, ...
KGM's user avatar
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2 votes
1 answer
213 views

How to transform a binary QP into an MILP?

I have a binary quadratic problem with objective ${\bf{x}}^T{\bf{Qx}}+{\bf{c}}^T{\bf{x}}$ subject to ${\bf{A}}{\bf{x}}\le{\bf{b}}$ ${\bf{A}}_{eq}{\bf{x}}={\bf{b}}_{eq}$. here ${\bf{x}}$ is binary. ...
KGM's user avatar
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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, ...
Mikkel Honningsvåg Sandhaug's user avatar
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58 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 ...
Lemma's user avatar
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3 votes
3 answers
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Do convex quadratic problems always have sparse solutions?

It is known that a feasible bounded linear program with $m$ constraints always has a solution with at most $m$ non-zero variables (a basic feasible solution). Since the number of constraints might be ...
Erel Segal-Halevi's user avatar
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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 \...
DSPinfinity's user avatar
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 ...
Tom Solberg's user avatar
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1 answer
154 views

Bilinear programming

Let us assume I have an optimization problem as follows: The first feasible region is an ellipsoid, meaning that a and b belong to a known ellipsoid. The second feasible region is polyhedral (a set ...
naghi pakdaman's user avatar
3 votes
0 answers
122 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 ...
Matheus Diógenes Andrade's user avatar
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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 ...
user900476's user avatar
1 vote
0 answers
38 views

Convex quadratic maximization over cartesian product of simplices

Suppose we are maximizing $f(x^1,\ldots,x^t)= \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}^\top Q \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}$ ...
independentvariable's user avatar
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 ...
user_lambda's user avatar
2 votes
1 answer
143 views

How to show that minimizing the epsilon-insensitive loss is equivalent to a quadratic program with inequality constraints?

This question is about an optimization problem that arises in support vector regression (SVR). Suppose you have $N$ pairs $(\vec{x}_n, y_n)$ as data and would like to find a vector of weights $\vec w \...
ForceBru's user avatar
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0 answers
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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 $\...
Lydia's user avatar
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5 votes
3 answers
217 views

Randomly constructing a bounded ellipsoid

In a project, I am working with constraints of the following type $$ \frac{1}{2}{x}^\top Q x + q^\top x + q_0 \leq 0 $$ where I randomly generate the data by (randn...
independentvariable's user avatar
2 votes
1 answer
84 views

epigraphs for quadratic constraints

I have a constraint of the following form \begin{equation} x^{\top}x + y^{\top}y \leq t \end{equation} where x, y are vector variables and t is a scalar variable. I can augment the variables x and y, ...
Kumar's user avatar
  • 153
3 votes
2 answers
217 views

Simplest Quadratic Programming algorithm for teaching

Can anyone recommend a straightforward quadratic programming (QP) algorithm suitable for an undergraduate engineering class? I'm interested in finding an algorithm that they can easily grasp and ...
Walton P. Coutinho's user avatar
0 votes
1 answer
108 views

Simulating an integer quadratic knapsack problem

I am trying to simulate the following quadratic integer program using $\textsf{cvxpy}$: $$ \begin{array}{ll} \underset {x_1, \dots, x_K} {\text{minimize}} & \displaystyle\sum\limits_{i=1}^{K}\frac{...
UserX's user avatar
  • 103
2 votes
1 answer
289 views

Looking for a reliable and scalable open source quadratic solver

In the convex optimization community, there has been a growing concern regarding the search for a reliable open-source solver (especially a quadratic programming solver) that can effectively deliver ...
Mohammad Namakshenas's user avatar
2 votes
2 answers
110 views

Potential methods for solving quadratic optmization problem

I am trying to solve a non-convex optimization problem with the help of sequential quadratic programming. I need to develop an algorithm inside SQP to solve this subproblem. What potential methods (...
Muhammad's user avatar
1 vote
1 answer
42 views

Non convex quadratic problem with complex variables

I am trying to solve a non convex optimization problem with the help of sequential quadric programing. My optimization variables are complex and I have expressions for gradients, hessian etc but all ...
Muhammad's user avatar
1 vote
1 answer
58 views

Quadratic optimization with non-constant coefficients

I have a series of functions (very similar to convex quadratic equations, see the first comment below) $f_1(x), f_2(x), \dots, f_n(x)$. Each of these functions touches the $x$-axis at $a_i$, which can ...
svanderk's user avatar
4 votes
1 answer
266 views

Solver for quadratically constrained mixed-integer linear programs

I have an optimization problem with vectors $x$, $y$, and $z$, where $x$ is an integer vector. My objective function is linear (i.e. $\|y\|_1$), but one of my constraints is quadratic ($x^Ty \leq z$). ...
Carol Eisen's user avatar
5 votes
2 answers
496 views

Simple OLS problem can only be solved in SCS. Is the dual infeasible?

Essentially, I am trying to solve a simple orthogonal least-squares (OLS) problem with some constraints — the coefficients must sum to $1$, no coefficient can be less than $0$, and no coefficient can ...
Pipob Puthipiroj's user avatar
3 votes
1 answer
223 views

How do I pass an objective bound to Gurobi?

I have a non-convex Quadratic Programming over unite simplex set. I have a valid lower bound on the objective function (goal is minimization problem). If I add a constraint like $$f(x)\geq lower~bound,...
Optimization Online's user avatar
-2 votes
1 answer
104 views

Converting a quadratic objective function in piecewise linear function

The objective function is of the form: $max$ $x^2/2+y^2/2+z^2/2$ I would like to convert it to piecewise linear function. How do I achieve that?
scouse_s's user avatar
1 vote
1 answer
121 views

How to model and solve such a 0-1 programming problem

My problem is described in this picture(It's like a Pyramid structure): The objective function is below: $$\min\sum_{k=1}^\ell\sum_{i=0}^{2^k-1}\sum_{j=0}^{2^k-1}\left(A_{i,j}^k-A_{i,j+1}^k\cdot\frac{...
happy's user avatar
  • 63
3 votes
2 answers
1k views

Is solving a quadratic programming optimization problem using python slower than C++?

I am using the cvxpy library in python to solve a quadratic programming problem and the solver used is scip. I found that when the amount of data becomes large, the solution process will be ...
happy's user avatar
  • 63
2 votes
1 answer
441 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 ...
jbuddy_13's user avatar
  • 551
3 votes
0 answers
148 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[...
christouandr7's user avatar
1 vote
2 answers
301 views

How to solve this mixed integer quadratic program using cvxpy or other method?

My problem is described in this picture: $$ \begin{array}{l} \left\{\begin{array}{l} \text { objective function: } \\ f = \min \sum_\limits{l=1}^2 \sum_\limits{i=0}^{2^l-1} \sum_\limits{j=0}^{2^l-2}\...
happy's user avatar
  • 63
2 votes
1 answer
390 views

Poorly conditioned quadratic programming with "simple" linear constraints

I have many quadratic programming problems of the following form: $$\min_{x\in\mathbb{R}^n} { \tfrac{1}{2} {\lVert Cx-d \rVert}^2} $$ $$\textrm{s.t.}\ x_1\le 0,\ x_n\le 0,\ x_n\le a_1^\top x_{1:n-1},\ ...
cfp's user avatar
  • 259
3 votes
2 answers
486 views

How to view pause and view current solution in CPLEX Optimization Studio?

I am solving my first model in CPLEX 22.1. I have setup a quadratic MIP with 100 variables and the model has been running for a day already with the best integer and best bound solutions barely ...
twaits791's user avatar
4 votes
0 answers
179 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 ...
kchnkrml's user avatar
4 votes
1 answer
508 views

Is this a non-linear integer model?

Let's say if I have two decision variables, $f$ and $g$ respectively, where $f$ is continuous, and $g$ is binary. If I have a constraint like this, $$ f\cdot g \le C$$ Does this make my model ...
overboxed's user avatar
  • 593
1 vote
0 answers
75 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. ...
worldsmithhelper's user avatar
6 votes
2 answers
239 views

When should we avoid linearizing a quadratic term?

Some solvers like Gurobi can handle mixed-integer quadratically-constrained quadratic models regardless of their nonconvexity. I have some experience that Gurobi can handle instances of the max $k$-...
Ramin Fakhimi's user avatar
10 votes
1 answer
504 views

Sensitivity analysis of QP

Given a quadratic program $$ f^* \equiv x^\top Q x + b^\top x \\ x \geq 0 \\ A^\top x = d \\ x \in \mathbb{R}^n $$ I would like to analyze the sensitivity of the solution $x^*$ to perturbations in $Q$ ...
ntrstd11's user avatar
  • 235
2 votes
2 answers
242 views

Difference between constraint formulation and performance

I am wondering about the characteristics and performance of some constraints with only binary variables. I assume that solving (integer) linear programs is faster than quadratic ones. At first: $$ a,b,...
Mike's user avatar
  • 147
1 vote
0 answers
266 views

Converting quadratic constrains to linear constraint [closed]

I try to convert a quadratic constraint to a linear one: $$ w_j = \sum w_\text{j,i} \\ w_\text{j,i} = \frac{w_j}{D} \times u \\ w_j,D,u \in \mathbb{N} \\ $$ The values for $w_j$ and $D$ are constant ...
Mike's user avatar
  • 147
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}...
orpanter's user avatar
  • 517
5 votes
3 answers
156 views

What is the go-to practical method for optimizing separable quadratic programs?

I have a quadratic program that looks like this: For fixed vector $b$, and matrices $A_1, ..., A_n$, Find column vectors $x_1, ..., x_n$ that minimize $\sum_{i=1}^n x_i ^T 1 1^T x_i$ subject to $\sum_{...
AspiringMat's user avatar
2 votes
1 answer
561 views

Can docplex solve a mixed integer quadratic programming (MIQP) problem?

I am trying to solve a mixed integer quadratic programming (MIQP) problem. The objective function contains the product of two continuous decision variables, some of constraints are non-linear too. I ...
GTek's user avatar
  • 307
5 votes
1 answer
214 views

How to handle a non-separable bilinear objective function in the special case of decoupled constraints?

I have a large number of (10000+) non-negative, real decision variables $x_i$ and $y_j$. Let $I$ and $J$ be the index sets associated with $x$ and $y$, respectively. Let $\bar{I}$ and $\bar{J}$ be non-...
Displayed_Name's user avatar