linear-programming

I am trying to write a linear program and need a variable z that equals the sign of x-c, where x is another variable, and c is a constant. I considered z = (x-c)/|x-c| . Unfortunately, if x=c, then this creates division by 0. I cannot use z=x-c, because I don't want to weight it by the magnitude of the difference between x and c. Does anyone know of a good way to express z so that it is the sign of x-c? Thank you for any help and suggestions! You can't model z = sign(x-c) exactly with a linear program (because the constraints in an LP are restricted to linear combinations of variables).

I have a few inequalities regarding {x,y} , that satisfies the following equations: x>=0 y>=0 f(x,y)=x^2+y^2>=100 g(x,y)=x^2+y^2<=200 Note that x and y must be integer. Graphically it can be represented as follows, the blue region is the region that satisfies the above inequalities: The question now is, is there any function in Matlab that finds every admissible pair of {x,y} ? If there is an algorithm to do this kind of thing I would be glad to hear about it as well. Of course, one approach we can always use is brute force approach where we test every possible combination of {x,y} to see

I am looking for an iOS library that enables solving LP, IP, BIP, MIP for an application I am developing. I've found GLPK but have no idea how to compile it for iOS, and after searching the web for some time, I did not find anything interesting... I'd appreciate if someone can help me how to compile GLPK for iOS or either knows of some open source LP solver for iOS. János I used GMP (GNU Multiple Precision Arithmetic Library) for iOS development, what is basically a C based static library for various mathematical purpose. I had to do calculation on a big matrix, so I needed a library that

A very similar questions were asked on SO already, but I couldn't find answer to the following problem. A linear maximization problem can be easily stated using for-all quantifier: obj = f(x) AND \forall x . Ax <= b => f(x) <= obj The queries like above can be posed to z3. Consequently I want to ask whether z3 is smart enough to recognize an LP problem when it sees one and will it apply a simplex method to eliminate a for-all quantifier? I did a few experiments and it seemed to work, but I haven't tried it on more complex examples. Thanks! Z3 does not recognize it as an LP optimization problem