# All Questions

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### Quasi-convex function must be “partially monotonic”?

$f(x)$ is quasi-convex, $$x^*\in\arg\min_{x\in C}f(x).$$ How to prove that, for any $a\in C$, $f(x)$ is weakly monotonic in the direction of $(x^*-a)$? Is this simple result a part of an ancient ...
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### Canonical form of a linear program

I have a linear programming problem that I want to write in the canonical form: \begin{align}\min&\quad c^\top X\\\text{s.t.}&\quad A\cdot X\le b\end{align} The problem is given by \begin{...
123 views

### How to implement a local search with different operators?

I read some papers on local search. I remark that several authors use different move operators. However, the pseudo-code I found on google only uses one operator. I am wondering how to implement the ...
103 views

### Why is this version of the algorithm more efficient?

I am a student self-studying Optimization, and I am reading about the Conjugate Gradient Method in Numerical Optimization by Nocedal & Wright, and they present two different algorithms for it. ...
109 views

### Convexity of the variance of a mixture distribution

$X$ is a random variable that is sampled from the mixture of uniform distributions. In other words: $$X \sim \sum_{i=1}^N w_i \cdot \mathbb{U}(x_i, x_{i+1}),$$ where $\mathbb{U}(x_i, x_{i+1})$ denotes ...
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### Mixing time exponent above threshold temperature for Glauber dynamics or annealing

It is well-known that the Glauber dynamics will converge in polynomial time to the Gibbs distribution for, say, the Ising model on a d-regular graph at high enough temperatures $T>T_c$. There are ...
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### Minimizing sum of functions with pairwise dependence

I have formulated a problem where I need to minimize the sum of $N$ functions, with only pairwise dependence between the functions (any single constraint involves only two functions having adjacent ...
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### How to model If $A \le B$ then $Y = 1$, otherwise $Y = 0$

Somehow I don't get it right. I would like to model the following conditional: If $A\le B$ then $Y=1$ otherwise $Y=0$ where $A, B$ are reals and $Y$ is binary. I can model as follows: $Y \cdot A \le B$...
85 views

### Finding primal feasible solution from optimal dual

I'm reading Boyd's notes on forming the dual problem in order to decompose the primal problem. On page 4, right before the start of the next section, he talks about how given the optimal dual solution,...
158 views

### Meta papers on operations research

Some time ago, I wrote this answer: https://or.stackexchange.com/a/3323/405 to a question here on this stack exchange. I've had similar discussions with colleges, but I never found anything written ...
44 views

### How to display the range of coefficients in docplex log?

A typical gurobi log can have a section where it shows the range of coefficients. Something like: ...
610 views

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

In evolutionary algorithms, two main abilities maintained which are Exploration and Exploitation. In Exploration the algorithm searching for new solutions in new regions, while Exploitation means ...
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### What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money $m$ to spend over $r$ different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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### Mixed integer programming vs Constraint programming

I see that certain studies are comparing MIP and constraint programming (CP) performances. And generally, they claim that CP outperforms MIP. But I believe that it is not completely true. Because ...
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### How to correct this scheduling algorithm?

I have a scheduling problem to solve. It's a resource-constrained project scheduling problem with time-varying resource availabilities. The objective is minimizing tardiness. The full detailed model ...
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### CPLEX keeps restarting in Pyomo

I tried running my model by adding the following settings to CPLEX. ...
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### knapsack problem with non-linear constraint

I have a basic knapsack problem where I need to fit the most weight possible in a bin: ...
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### CPLEX MIP warm start seems slow down the program?

I have been working on a combinatorial optimization problem which can be modeled as an integer linear programming. I implemented it as a c++ project in visual studio 2017 and CPLEX1271. With the hope ...
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### Scenario based approach to value-at-risk optimization using mixed-integer programming

For a discrete set of scenarios, minimising value at risk can be formulated as a mixed integer linear programming problem. If each scenario has equal probability then this can be written as \begin{...
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### How to optimize a utility function that contains step function?

I have an optimization problem with an uncommon utility: to find a $\beta$ that maximizes $$r^{T}\cdot H(X\cdot\beta)$$ where $H()$ is a Heaviside step function as in wiki $r$ is a vector of size ...
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### How to linearize a quadratic constraint to add it then via a callback function

Suppose we have a positive continuous variables $0 \le x \le UB$ where $UB$ is a known upper bound. How can we linearize the term $x^2$? Detailled problem: Suppose that via a callback we compute a ...
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### Multiple Knapsacks with splitting

I am trying to solve a problem that I believe is a variation of the multiple knapsacks. Like the classical multiple knapsacks problem, I have a set of items, each one with a weight and a value and I ...
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### Is there any OR way to solve this problem?

For each observations there are 207 variables (binary, either a 'symptom' happened or not), class variable is also binary. For each variable or symptom there is a weight attached (currently set ...
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### Possibility of indexing decision variables with 2 indices using a set of tuples in Pyomo

I am currently attempting to solve a network problem that is not fully connected.Thus, I have attempted to do some preprocessing of data so as to form a set of tuples, e.g. $\{(a,b), (c,e),\ldots\}$, ...
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### How to balance the workload of teachers in OR-Tools (maximization of the minimum)

I am very new to optimization and OR-Tools. I am trying to solve a very simple question. Let's assume that we have $n$ students. Each student needs to be assigned to only one teacher as a supervisor. ...
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### Decision variable transformation in Gurobi

I'm trying to find a way of setting the values of a binary MVar object (which is my decision variable) of size n to {-1,1}. Right now I have a vector that can either take values 0 or 1 (due to binary ...
176 views

### How to find all vertices of a polyhedron

I have a convex polyhedron given by a set of linear inequalities, for example: $$x_1 \geq 0,~~ x_2 \geq 0, ~~x_3\geq 0 \\ x_1+x_2\leq 1,~~ x_2+x_3\leq 1,~~ x_3+x_1\leq 1$$ I want to list all the ...
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### View of Constraints and Decision Variables in Pyomo

I have just attempted to construct my first Pyomo model. However, I was unable to locate any documentation that shows how to view constraints, decision variables. As my model is big, I need to see ...
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### Can we use reinforcement learning and convex optimization to solve an optimization problem?

For an optimization problem, there are multiple-type variables should be optimized. Can we use the convex optimization method to solve a subproblem of partial variables, and then, with the obtained ...
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### Conditions required for strong duality to hold for SDPs

According to Wikipedia, strong duality holds when "the primal optimal objective and the dual optimal objective are equal." What are the necessary conditions for strong duality to hold in ...