[Help-glpk] [Fwd: Some questions about convexity of LP]

[Andrew Makhorin]

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From: sermsak <address@hidden>
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Subject: Some questions about convexity of LP
Date: Sat, 01 Mar 2014 13:42:34 +0700

Dear all,

Consider the LP,
        min a'x + b'y
        s.t.
        Px + Qy + r = 0
        x_lb <= x <= x_ub
        y_lb <= y <= y_ub
where x,y,r are vector in R^n, P,Q are n x n matrices.
x_lb, x_ub, y_lb, y_ub are bounds of x, y.

Q1. 
My guess is that the intersection of the feasible region of the problem
and the hyper plane (x_k, y_k) where (x_k,y_k) are member of x and y, 
is a convex polygon. Is it always true?

Q2. How can one find such intersection area?
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s.s.