# Tagged Questions

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### Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
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### Linear Optimization Study Material

I've recently enrolled in a linear optimization course, and it's been a while since I've taken linear algebra. I do not yet have access to the book for the course or I would skim it to see what I need ...
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### References on constrained least square problems?

I have met some constrained least square problems, for example, my last post. I found that there are various methods for slightly different constraints, and still I often had little clue about how to ...
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### Reference request, discrete optimization problem

i am not an expert in optimization. I have stumbled across an interesting problem which looks to me like there should already exist literature about it. The problem can be phrased as follows: given ...
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### “Cookbook” methods for neighborhood structure design in simulated annealing for combinatorial optimization?

What are some "cookbook" methods for neighborhood structure design in simulated annealing for combinatorial optimization? Are some reviews or books that contain some "cookbook" methods for ...
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### Simple example application of Karush-Kuhn-Tucker conditions to minimization problem

I am wondering if there is a simple example application of the Karush-Kuhn-Tucker conditions to show that a minimum exists for a multivariate minimization/optimization problem. Could anyone suggest a ...
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### Book on constrained numerical optimization

For unconstrained numerical optimization I have been using the book "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" by Dennis and Schnabel. I found it to be a great book ...
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### Degeneracy of the analytic center of a set of linear inequalities

I have a question about the degeneracy of the analytic center of a set of linear inequalities. When the set of linear inequalities is degenerate, I guess that the analytic center would also be ...
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### Convex programming when the problem has an underlying combinatorial structure that's a DAG

I have a nonlinear convex objective function to minimize. The function is defined on a set of variables: $\{ x_1,x_2, \ldots ,x_p \},$ where each $x_i$ is a number associated with a path in the DAG. ...
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### A convex programming problem involving sum of logarithms of linear functions

Here is a convex programming problem I encountered while working on an estimation problem for a mixture of multinomial distributions. We have a matrix $A_{m \times n}$ containing non-negative real ...
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### Specific solvable cases of TSP

Did a quick search on polynomial time solvable TSP and found some references such as this one for special cases for the bottleneck TSP. Was wondering if anyone was aware of any references that catalog ...
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### Looking to understand the rationale for money denomination

Money is typically denominated in a way that allows for a greedy algorithm when computing a given amount $s$ as a sum of denominations $d_i$ of coins or bills:  s = \sum_{i=1}^k n_i ...
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### Linear Programming Books

Do you know of a good book on linear programming? To be more specific, i am taking linear optimization class and my textbook sucks. Teacher is not too involved in this class so can't get too much help ...
Let $\mathbf{x} =$ {$x_{i}$} be a set of $n$ positive reals. In every good book on inequalities, one finds the classical result \begin{eqnarray} AM(\mathbf{x}) \geq GM(\mathbf{x}) \geq ...