# Tag Info

### PhD-level textbooks on linear programming

A classic textbook that does a really good job of building from the fundamentals is Theory of Linear and Integer Programming by Schrijver. Chapter 7 in particular gives great intuition on linear ...
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### IPOPT with HSL vs MUMPS

This question happened to appear only a couple days after Byron Tasseff, Carleton Coffrin, Andreas Wächter, and Carl Laird (the last two are the original authors of IPOPT together with Larry Biegler) ...
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### How to reduce an LP problem already in its standard form?

Concept The tools you are referring to are commonly called presolvers. Resources (Implementation) / Availability Every optimization software makes use of those (to improve performance, but also ...
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### PhD-level textbooks on linear programming

I used to study with the following book: Chvatal, V. (1983). Linear programming. Overall it's very clear. It's written primary for graduate courses in operations research, math and computer science....
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### PhD-level textbooks on linear programming

G.B. Dantzig and M.N. Thapa Linear Programming 1: Introduction, Springer, 1997 and Linear Programming 2: Theory and Extensions, Spinger, 2003. Linear Programming 2, Theory and Extensions, is the one ...
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### Simplest way to eliminate redundant constraints due to a new cut

As a partial answer, Telgen (1977) has shown that eliminating all redundant inequalities is LP-equivalent, i.e. in general not easier than solving linear programs. Clearly, this does not exclude ...
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### Algorithms for sparse linear systems

The following isn't meant to be exhaustive. It usually depends on the structure of the matrix because that impacts the way you choose it. In general there are sparse variants for many of the general ...
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### PhD-level textbooks on linear programming

There are some good problems in Linear Optimization: Theory and Extensions by Fang and Puthenputra. Chapter 2 of the book ("Geometry of Linear Programming") is most comparable to Chapter 2 of ...
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### Convexity of a QP

Some quadratic problems are convex while others may not. This is a nice discussion in the QP by Erwin Kalvelagen.
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### Can't understand K-Truss Graph properties

The definition of a k-truss you are working with seems to deviate from the 'standard' definition. See below for a few different definitions that boil down to the same thing. A k-truss of a graph $G$ ...
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### Computing simplex tableu for a given basis

Yes, the formula is the same regardless of whether you are maximizing or minimizing. The difference is in how you interpret the reduced costs $c^\prime -c_B^\prime B^{-1} A.$ When maximizing, you want ...
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### Optimizing for an unknown conjugation matrix

I am not sure a unique solution exists (consider the one-dimensional case for example), nor a closed-form one. An approach to (approximately) solving your problem is to first reformulate it as: \...
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### Convexity of a function

The sum of convex functions is convex!
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1 vote
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### Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$

The conjugate gradient method works quite well on least square problems and is easy to implement. With a simple line search, it should be much better than a simple gradient descent. There are many ...
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