# Questions tagged [convex-optimization]

Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum.

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### Black-box optimization of a single parameter function with high cost evaluation

I need to solve a series of single parameter black-box minimization problem. The underlying cost functions are quite simple. They always have the same shape: a global minimum inside a fixed interval (-...
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### What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I ...
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### Is $\min \ x^3 \ \mathrm{s.t.}\ x \geq 0$ a convex problem?

The problem $$\min \ x^3 \ \mathrm{s.t.} \ x \geq 0$$ is sometimes said to be a convex optimization problem. $f(x) = x^3$ is not a convex function. However, in the domain of $x\geq 0$ it is convex. So ...
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### How to mathematically formulate the optimization problem?

I have a system with $S$ service points. There are also $U$ users in the system. We have $$U>S>G$$ One group can have maximum $M$ service points, but there is no restrictions on the number of ...
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### Correct way to define constraints in Pyomo

Can I know if the constraint below can be defined as follows in Pyomo for convex optimization. W and G are arrays of dimension M x N. ...
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### Can I define constraints in Pyomo as a list?

I would like to define the following constraint in Pyomo $$W^\top{\bf 1}\le\hat w=\begin{bmatrix}\hat{w}_1&\hat{w}_2&\ldots&\hat{w}_N\end{bmatrix}^\top$$ where $W$ is a $2\times4$ matrix. ...
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### Hyperbolic constraint as second-order cone

I have a problem which simplifies to: \begin{align} \max w &\\ w&\le xy \\ x,y&\le10 \\ x,y&\ge0 \end{align} Recognizing that $xy$ form a hyperbolic constraint, I can solve by ...
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### How can I express this max-min in CPLEX?

Initially, I had the below objective function $\max \sum_{u=1}^{U}\sum_{c=1}^{C}x_{u,c}d_{u,c}$ where $x_{u,c}$ are optimization variables I modelled this in CPLEX as ...
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### Oscillations with (online) mixed-integer optimization problem

I have the following mixed-integer optimization problem: \begin{aligned} \max_{x,y} \quad & \sum_i x_i - \|wx\|_2 \\ \text{s.t.} \quad & \sum_i x_i \leq A \\ \quad & x \leq x_{\max} y \\ ...
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### Model definition in pyomo to solve online optimization problem

I am trying to model the attached online optmization problem in pyomo. Eventually, I am going to use the octeract solver to find the matrix soluions of W and G. I would like to ask advice about ...
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### How to define a stationary point of the MINLP problem?

As we all know, KKT point and stationary point are well defined when the optimization variables are continuous in the problem. Now, I want to know whether there exist some special points except for ...
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### complexity order of the interior point method

I was wondering why the complexity order of the interior point method is O()^3 or O()^3.5? Much appreciate your time and consideration.
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### How to linearise this nonlinear constraint?

I have a constraint in the form $\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$ where $x_{m,n}$ is binary variable $t_u$ and $\beta_u$ are continuous optimization ...
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### Recommended python solver for an online optimization problem

I need to implement a load scheduling algorithm that involves solving an online optimisation problem from a research paper for my Real time systems course. This convex optimisation problem is setup ...
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