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

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### Are there any real-world problems where quadratization helps to solve something that couldn't have been solved without quadratization?

The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the ...
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### CPLEX non-convex Quadratic Programming algorithms

CPLEX solves non-convex quadratic problems to global optimality with a global optimality option (in version 12). The relevant pages are this and this. I benchmarked many solvers, and see that CPLEX ...
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### Assignment problem where assignments must be done sequentially

I have a weird planning problem. I think it falls under the assignment category, but I'm not sure because I'm not familiar with assignment problems, and also because there is a "temporal" angle to it, ...
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### How can I linearize or convexify this binary quadratic optimization problem?

I have an optimization problem as below. I am having a hard time with the last constraint. $\max \eta$ subject to ${\bf U}(:,m)^T{\bf A}{\bf U}(:,m)=0,m=1,2,\cdots,M$ here $\bf{A}$ is a Binary ...
Let $l,u\in\mathbb{R}^n$, and consider the QP: $$\min_{l\le x\le u} {(\Delta x)^\top (\Delta x)}$$ where $\Delta x=[x_2-x_1,\,x_3-x_2,\,\dots,\,x_n-x_{n-1}]^\top$. I.e. we want to minimize the squared ...
I would like to linearize $x^2$ term in my objective function. I understand this can be solved using quadratic programming solver; however, for my use case linearization is necessary to convert it to ...