# Tag Info

Accepted

### Why does some solvers can only solve conic optimization problems?

The fundamental algorithm employed by Mosek and SeDuMi is a primal-dual interior-point algorithm based on the work of Nesterov and Todd (NT). See for instance my paper and the references therein. This ...

### What is the best open source solver for large scale LP optimization in pyomo?

There is a new open source solver that looks quite promising, HiGHS: https://www.maths.ed.ac.uk/hall/HiGHS/ But as pointed out by others, for mixed-integer programming problems, at the moment, open-...
Accepted

Accepted

### Determining the optimize lambda in Multi-Objective Optimization

There is no mathematical way to derive (or justify) a value for $\lambda$. The justification has to be made in the context of a specific problem and a specific (reasonably credible) decision maker. ...

### How to make following constraint a convex one?

The constraint is not convex, and is not transformable to a convex constraint without substantively changing it. The additive linear term $dx$ is irrelevant to convexity. So let's ignore it and look ...

### What does nonconvex multilinear mean?

Non-convex means not convex, which could mean concave but also neither convex nor concave, such as a bilinear term $xy$.

### Fast way to repeatedly solve many similar LPs/QPs in parallel

The OPTMODEL modeling language in SAS (disclaimer: I work at SAS) supports two features for solving independent optimization (LP or otherwise) problems concurrently: The COFOR loop, which ...

### Maximize correlation subject to nonconvex correlation constraints

You could add the non-convex constraint $z^Tz = 1$. That would make the objective function and other constraints linear. So this would be a Linear Programming problem, but for a single non-convex ...
Accepted

### How to find the index of the item, the first time appears?

Here's a formulation if at least one $x_i$ must be $1$: \begin{align} \sum_i y_i &= 1 \tag1\label1\\ y_i &\le x_i &&\text{for all $i$} \tag2\label2\\ y_i &\le 1-x_j &&\text{...

### Determining the optimize lambda in Multi-Objective Optimization

Another approach could be generating the Pareto Frontier, solving the problem several times for different values of lambda, using a Weighted sum algorithm (see this or this).

### Difference between exploration and exploitation in Simulated Annealing algorithm

I personally see it as follows. In simulated annealing the likelihood of choosing a solution from the neighborhood is quite high at the beginning. This phase could be regarded as exploration as the ...

### Convex Maximization with Linear Constraints

The location-inventory problem by Shen, et al. and Daskin, et al. has a concave minimization objective. It's related to economies of scale (which you list in your PS 2) but not exactly the same.

### Disciplined convex programming representation of $x\sqrt{1-x}$
This is possible purely under DCP. As you are interested in the interval $[0,1]$, rewrite your function as $$x\sqrt{1-x}=\exp\left(\ln x+\frac12\ln(1-x)\right),\quad x\in[0,1].$$ Then the following ...