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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17 views

Method of Multipliers: Why is the next iterate always dual feasible?

I am reading this expository paper on ADMM by Boyd, et. al. Consider the problem \begin{align*} &\min f(x)\\ & \ \text{s.t.} \ \ \ Ax = b \end{align*} with Lagrangian $L(x, \lambda) = f(x) + \...
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0answers
22 views

Recovering Primal Solution from Dual solution

Consider the problem \begin{align*} &\min f(x)\\ & \ \text{s.t.} \ \ \ Ax = b \end{align*} In this expository paper, Boyd claims (top of page $8$) that if: $\lambda^*$ is a dual optimal ...
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0answers
26 views

Length of intervals in Fibonacci Line Search

I am self-learning basic optimization techniques and trying to implement the 1-dimensional line search algorithms from the book - Algorithms for Optimization by Kochenderfer and Wheerler, MIT Press. I ...
2
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2answers
106 views

What kind of scheduling/packing problem is this?

I have the following problem which seems to be a mixture of a resource constrained scheduling and packing problem. There is a set of activities $A_1,\ldots,A_n$ and given precedences $P$, where $(A_i,...
3
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1answer
88 views

Finding the global minimum of $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$

I am self-learning optimization algorithms. A certain assignment problem is as follows: Show that the $n$-dimensional function $f(\mathbf{x})=\|(1-x_1,x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n,x_n-2)\|_2^2$ ...
0
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1answer
70 views

How to solve this clustering problem with heuristic or meta-heuristic approach?

I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-...
1
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1answer
46 views

Integral of PWL-Constraint in Gurobi (Java)

In my optimization model, I use piecewise-linear constraints with the output of $y[m]$. The question or problem I have now is whether there is a way in Gurobi (Java) to form the integral for this PWL ...
3
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1answer
44 views

Non-Convex QCP model - Used Method in Gurobi

I have the following question: I have a non-convex QCP model. In the parameter description for method it says that "Only barrier is available for continuous QCP models". However, the dual ...
2
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1answer
64 views

Accessing Lagrange Multipliers in CPLEX

I want to get the lagrange multipliers for a solution from cplex. I am using it via Python. The problem is continuous with a linear objective function and elements of solution vector $x$ are ...
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2answers
95 views

Why do we need SCED in addition to SCUC in RTO/ISO electricity markets?

I understand that we use SCUC (Security Constrained Unit Commitment) and SCED (Security Constrained Economic Dispatch) in day ahead electricity market – According to the literature, SCUC is used to ...
4
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1answer
301 views

Is there any automatic way to spot contradictory constraints in linear programming?

Let's have the following trivial linear program: \begin{align}\max&\quad z=20A+30B\\\text{s.t.}&\quad A\le60\\&\quad B\le50\\&\quad A+2B\ge220\\&\quad A,B\ge0\end{align} It's easy ...
5
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2answers
74 views

MAX-CUT: are there any algorithms or codes for classical computers, that cater to this specific case?

I missed the opportunity to ask this on OR.SE by 24 days! I asked it at CS.SE on 6 May 2019 and OR.SE entered Private Beta on 30 May 2019. It's a problem about minimizing a sum of terms that are ...
2
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1answer
92 views

How to deal with log0 in optimization problem

I am adding some constraints to my model described in my previous post, where a discontinuous piecewise-quadratic functions is the objective to be minimized in cvx. Here I have an additional terms, ...
5
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1answer
173 views

Subtour elimination constraint in Travelling Salesman Problem

I am trying to understand travelling salesman problem, the Dantzig, Fulkerson, Johnson(1954) formulation. In the general formulation given below I am having trouble to implement subtour elimination in ...
3
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2answers
143 views

How to reformulate a discontinuous piecewise-quadratic functions

I am trying to develop a model, solving an optimization problem which has the following objective function: variable p(i); minimize sum(cost) subject to p>=0 ...
1
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1answer
38 views

How to interpret no-overlap constraints with rotation as a mixed integer programming

Suppose, we want to locate some given facilities $\left \{ (i,j) \ |\ (i,j) \in \text[{1,\cdots, N}]\right \}$ in a specific area. Each facility has a predefined dimension with a length $l_{i}$ and ...
2
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2answers
71 views

Relationship aware task scheduling heuristics

I have a task scheduling/assignment on machines problem (like a classic bin packing problem) with a twist in which the placement/assignment of one task affects the placement/assignment of other tasks (...
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0answers
53 views

Quadratic optimization in Gurobi with constraint

I have a question of understanding in Gurobi: I have an objective function in which my optimization variable x is squared. I have solved this bsiher by a quadratic objective function with $x$, $x$. ...
3
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3answers
100 views

warmstarting simplex algorithm- how much can problems differ from each other?

I'm working on an implementation of the simplex algorithm. I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem. I couldn't really say ...
3
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1answer
44 views

Control & Experimental Group Selection Methodology using STDEV and T-Test?

I would like to know if my methodology was 'correct': I am trying to conduct an experiment on my stores. I would like to find out the effect of a marketing campaign on the number of transactions. Only ...
2
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1answer
157 views

How to convexify log(convex) function?

I have the following optimization problem: \begin{align}\max_x&\quad\log_2(1+|a+bx|^2+cx^2)\\\text{s.t.}&\quad0\le x\le1\\&\quad(1-x^2)\ge\text{constant}\end{align} where $a$ and $b$ are ...
3
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3answers
655 views

Model if-else statement

I need to build a if-else constraint for this statement, where $x_P$ and $x_I$ are decision variables, and $C$ is a constant: if $x_P \ge C$ then $x_I = x_P - C$ else $x_I = 0$. Any help is greatly ...
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1answer
48 views

Find an upper bound for an objective function

My objective function is $\log_2(1+{x^2y^2})$ and I found two upper bounds for $x^2$ and $y^2$. For example, assumed that we have the following upper bounds: $x^2\leq\text{constant}_1^2$ and $y^2\leq\...
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1answer
113 views

fpl and constraints about centers

Does anybody know how we could optimise fpl problems with additional constraints?
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1answer
108 views

Invalid solutions to Piecewise Mccormick Envelope Implementation

I am currently trying to implement a piecewise McCormick envelope in Drake (c++). The current issue I am having is that the solution produced by the optimization does not produce a valid $x$ and $y$ ...
2
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3answers
120 views

Linearizing a Max Function in the constraint - not working

I have a minimization function which is in its simplest form looks like below. I am including the index of the variables. ...
5
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2answers
88 views

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 ...
4
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2answers
193 views

Mixed-integer optimization with bilinear constraint

So I have an optimization problem of the following form: \begin{aligned} \max_{x,y} \quad & \sum_i x_i \\ \text{s.t.} \quad & \sum_i x_iy_i \leq a \\ \quad & x_{\min} \leq x \leq x_{\max} ...
3
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1answer
64 views

Clustering problem involving multidepots and customers requiring commodities located exclusively in an specific depot

I'm trying to solve a clustering problem that's similiar to a VRP Pickup and Delivery problem with multiple depots and customers. Each customer demands a commodity that is exclusively found on one ...
2
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1answer
67 views

Impose binary constraint on integer matrix with CVXPY

So I have the following matrix: \begin{equation} P_{i,j}= \begin{bmatrix} x_0 & x_1 & x_2 \\ y_0 & y_1 & y_2 \\ z_0 & z_1 & z_2 \end{bmatrix} \end{equation} where ...
1
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1answer
76 views

Relation between order quantity and average cycle stock

Annual demand: $1000$ units Unit cost: $5$ dollars Company replenishes the inventory two times per year. Average Cycle Stock: $300$ I am asked to compare average cycle stock with number of ...
6
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2answers
157 views

Index of element in MILP vector decision variable that equals 1

Consider a decision variable in a MILP constrained: $$\sum_i p_i = 1$$ $$p_i\ \in \{0, 1\}$$ Obviously one element in $p$ is 1 and all others are 0. How can I set a decision variable to the index i of ...
3
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1answer
152 views

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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0answers
77 views

Mixed Integer Programming - Model Formulation for A Resource Allocation Problem

There are a number of orders, which needs to be shipped. For each order, there may be 1 to 3 route options. The problem here is to find out the best allocation (combination) of orders among these ...
2
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0answers
29 views

How to use NEOS without using Pyomo

I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
2
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1answer
43 views

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 ...
2
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0answers
53 views

How to model non-zero minimum constraint?

I found following way to model a minimum constraint but in my case I need a non-zero minimum value. So in this figure, if any value of x_i is 0 then answer is 0 (assume x_i >=0) but I need non-zero ...
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1answer
89 views

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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0answers
147 views

Is there any Operations Research group in Clubhouse?

Since the introduction of the Clubhouse app, there are several groups on different topics and people can talk about specific topics in different fields. Is there any group related to "Operations ...
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0answers
74 views

MILP formulation for “if (a>=b) then c=1, 0 otherwise”

I need to build a MILP (Mixed integer linear programming) constraint form this if-else statement. In my formulation a and b are two continuous variables and c is boolean. if (a >= b) then c = 1, 0 ...
4
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1answer
149 views

how to implement an optimization function with polynomial in Gurobi (Java)

I have the following problem: I have an objective function with the optimization variable $x$, which looks simplified like this: $ZF = (a+b)*(x+1)$ Here $a$ is simply a constant value. However, behind ...
0
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0answers
40 views

Linear equation from pairs of values with conditions in Gurobi (Java)

How can I create a linear equation in Gurobi (Java) from values (x-y value pairs) that also has the following properties: $\forall x \leq 0 \Longrightarrow y = 0$ The linear line/equation should have ...
9
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4answers
562 views

Recommendations for OM blogs

Could someone suggest good blogs to follow for researchers in Operations Management/ Supply Chain Management /Operations Research?
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1answer
128 views

if-else query depending on optimization variable in Gurobi (Java)

I am looking for the most elegant solution to the following problem: I have an if-else query that depends on my optimization variable $x_i$. If $a \leq b_i + x_i$, the parameter $c$ should take the ...
8
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5answers
639 views

Paper suggestions on local search algorithms

I am looking for papers (or any resources) that go deep into the details of implementing local search algorithms. I don't want an introductory paper on the subject. Rather, I would prefer a survey ...
5
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1answer
111 views

Maximize number of backups that fit on backup drive

This is an intrinsically "practical" question, but it leads to a well-defined mathematical problem. Let me start with the practical part: I regularly back up my data. My backup strategy are ...
2
votes
1answer
62 views

Constraining flow into a node and out of a node using Min Cost Flow input

Let's say I have a graph $G=(V,E)$ where each vertex has an edge going both into and out of it (i.e. cyclic, akin to the kidney donor pair problem). Now suppose we have a capacity $u_{ij} = 1 \forall(...
3
votes
1answer
110 views

Min Cost Flow with lower bound reduction to MCF algorithm

We define the Min Cost Flow Problem with Lower Bounds (MCFPLB) as a generalization of the usual Min Cost Flow. The input consists of: a directed graph $G=(V,E)$ capacities $u_{ij} \geq 0$ for each ...
2
votes
3answers
78 views

Link a binary variable to continuous variable in Java Gurobi

I have the following problem: Depending on my continuous optimization variable $S_m$, I would like to introduce a binary variable $x_m$, which, depending on the value of $S_m$ (greater or less than 0) ...
5
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3answers
1k views

How does a solver generally know whether a solution is optimal?

I was wondering how does the solver for a MILP determine whether a solution is optimal. I am having a hard time to believe that the solver actually tries all solutions, since in some cases I have over ...

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