# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### Minimizing $x_1/x_2$ over a simplex in the positive orthant

I need to solve the following problem \begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix. The best thing I can think ...
147 views

### Heuristic Search Planning Tree Leading to Worse TSP Solutions than Naive Greedy

I'm doing a Traveling Salesman Problem (TSP) homework for a coursera optimization course. My first attempt was a regular naive greedy approach, from each point, moving to the closest node (that hadn't ...
160 views

### Modeling Linear Program to decide if an inequality is facet

Suppose you have a set of points $v_1,\ldots,v_n$, which are the vertices of the polytope $P=\operatorname{conv}\{v_1,\ldots,v_n\}$ and a linear inequality $a^\top v \leq b$. What would be a linear ...
2k views

### Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer ...
84 views

### How to convert non-normal probabilistic constraints to deterministic ones for mathematical modelling?

I am working on a chance-constrained optimisation model that takes into account uncertainty. I am aware of how to convert constraints that are of a probabilistic nature into the equivalent ...
87 views

### Analytically finding the maximizer of a trace optimization problem

$A \in \mathbb{R}^{m \times n}$ is an arbitrary data matrix. Moreover, $w \in \mathbb{R}^m$ is a data vector which is a probability vector, i.e., $w\succeq 0, \sum_{i=1}^m w_i = 1$. I have a ...
35 views

### Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
121 views

### Dual variables associated with same equation for different time instants

I have three equations that are essentially the same equation defined for three time instants. The equations are basically calculating the state of energy of an energy storage facility. \begin{align} ...
48 views

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### What is the difference between optimization software APIs based on performance and speed?

The state-of-art solvers like CPLEX or Gurobi and some of the open-source solvers have had the different APIs (like Python, C/C++, Java, etc.) in which users could write their MP model in own ...
87 views

### How to minimize a weighted sum of RMSE-like terms?

I am trying to solve the following problem: \begin{align} \min&\quad f(x) = \sum_{i=1}^{n}{a_ix_i} + \sum_{i=1}^{n}{b_i\sqrt{\sum_{j=1}^{m}{\left(y_{i,j}-x_i\right)^2}}}\\\text{s.t.}&\quad x_{...
44 views

### defining Mixed integer linear inequalities for a set of variables

The problem is described as follows: considering $n$ variables which are continuous and bounded such that $$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.$$ How can i define a set of mixed integer ...
3k views

### Is it necessary to study rigorous math courses in OR?

I am a business student with engineering background and I am studying papers published in some journals like Management Science, Operations Research, Math of OR and they use some notations and ...
622 views

### Bin packing variant

I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
953 views

I want to solve a linear programming minimax problem here mathematically without using software: \begin{align*} \text{min}\ \text{max} \quad & \{x_1,x_2,x_3\} \\ \text{s.t.} \... 0answers 51 views ### Semi-definite Programming, non standard notation The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is: \begin{array}{cl} \min & c^\top x \\ \mathrm{s.t.} & 0 \succeq ...
I'm trying to implement the following in AMPL: $$i \in [N], j \in[N] \backslash \{i\}, t \in [T]$$ I have so far written the following: ...