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 ...
• 11
1 vote
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• 2,377
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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, ...
• 2,377
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. ...
• 2,377
1 vote
60 views

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, ...
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 ...
• 23
922 views

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 ...
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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 ...
• 101
1 vote
38 views

Convex quadratic maximization over cartesian product of simplices

Suppose we are maximizing $f(x^1,\ldots,x^t)= \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}^\top Q \begin{bmatrix}{x^1}^\top & \ldots & {x^t}^\top \end{bmatrix}$ ...
• 3,980
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
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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...
• 3,980
84 views

I have a constraint of the following form $$x^{\top}x + y^{\top}y \leq t$$ where x, y are vector variables and t is a scalar variable. I can augment the variables x and y, ...
• 153
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 ...
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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?
1 vote
121 views

1 vote
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• 259
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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 ...
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 ...
• 41
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 ...
• 593
1 vote
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. ...
• 4,037
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 $k$-...
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 $Q$ ...
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• 147
1 vote