# 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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### 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
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### 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 ...
• 513
1 vote
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### 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. ...
• 3,898
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### 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 $k$-...
127 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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### Bilinear programming vs Mixed integer linear programming performance comparison

I know that both bilinear programming and mixed integer linear programming are NP-hard. But is there a preference to have when choosing an approach to solve a problem that can be represented in both, ...
• 173
121 views

### How to exponentiate binary variables in QUBO-type problems?

Ising Model In an Ising model, the Hamiltonian of one configuration of spins $\vec{s}$ is: $$H(\vec{s}, \mathcal{J}, \mathcal{h}) = \sum_{i} h_{i} s_{i} + \sum_{i \ne j}J_{ij} s_{i}s_{j}$$ where ...
• 523
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### Inverse Ising problem

Inverse Ising Problem The inverse ising problem means fitting the coupling $J_{ij}$ and field $h_{i}$ parameters given a sample of configurations of spins. Each spin $s_{i}$ is either +1 or -1. The ...
• 523
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### How do I formulate constraints that check if a parameter is between certain values, using binary variables?

I have $3$ parameters $a_1,a_2,a_3$ and a variable $d$ and $3$ binary variables $b_1,b_2,b_3$ and a "result" variable $s$. How do I model constraints so that: If $d$ is between $0$ and $a_1$...
• 43
1 vote
80 views

### Optimisation Multiple Constraints

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is \...
73 views

### Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program

I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function: \begin{equation} x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
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### Non RLT-Cutting planes for nonconvex QPs?

Consider a general nonconvex QP $x^\top Qx$. This can be linearized in an extended space by using the variable $Y=xx^\top$. Now a valid inequality $a^\top x \le b$ can be strengthend by the RLT ...
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