Detailed Steps of the Fourier-Motzkin Elimination
نویسندگان
چکیده
This file provide the detailed steps for obtaining the bounds on R1, R2 via the obtained results on (R1c, R1p, R2c, R2p). The rate pair (R1c, R1p, R2c, R2p) is achievable if it satisfies following inequalities. R1c ≤ rank(U 1 H11V21) (1) R1p ≤ m1 − r21 (2) R2c ≤ r12 (3) R1c +R1p ≤ r11 (4) R1c +R2c ≤ r12 + rank(U 10H11V21) (5) R1p +R2c ≤ r12 + rank(U 10H11V20) (6) R1c +R1p +R2c ≤ n1 (7) R2c ≤ rank(U 2 H22V11) (8) R2p ≤ m2 − r12 (9) R1c ≤ r21 (10) R2c +R2p ≤ r22 (11) R2c +R1c ≤ r21 + rank(U 20H22V11) (12) R2p +R1c ≤ r21 + rank(U 20H22V10) (13) R2c +R2p +R1c ≤ n2 (14) where (3) is implied by (8) as rank(U 2 H22V11) ≤ rank(V11) = r12. Similarly, (10) is implied by (1). Removing the redundant inequalities and substituting with R1p = R1−R1c, R2p = R2−R2c,
منابع مشابه
Combinatorial properties of Fourier-Motzkin elimination
Fourier-Motzkin elimination is a classical method for solving linear inequalities in which one variable is eliminated in each iteration. This method is considered here as a matrix operation and properties of this operation are established. In particular, the focus is on situations where this matrix operation preserves combinatorial matrices (defined here as (0, 1,−1)-matrices).
متن کاملEla Combinatorial Properties of Fourier - Motzkin Elimination
Fourier-Motzkin elimination is a classical method for solving linear inequalities in which one variable is eliminated in each iteration. This method is considered here as a matrix operation and properties of this operation are established. In particular, the focus is on situations where this matrix operation preserves combinatorial matrices (defined here as (0, 1,−1)-matrices).
متن کاملStrong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier-Motzkin Elimination Approach
The Fourier-Motzkin elimination method has been recently extended to linear inequality systems that have infinitely many inequalities. It has been used in the study of linear semi-infinite programming by Basu, Martin, and Ryan. Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang recently published in Optimization, which states “all the duality res...
متن کاملTropical Fourier-Motzkin elimination, with an application to real-time verification
We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical analogue of Fourier-Motzkin elimination from which we derive geometrical properties of these polyhedra. In particular, we show that they coincide with the tropicall...
متن کاملParallel Fourier-Motzkin Elimination
Fourier{Motzkin elimination is a computationally expensive but powerful method to solve a system of linear inequalities for real and integer solution spaces. Because it yields an explicit representation of the solution set, in contrast to other methods such as Simplex, one may, in some cases, take its longer run time into account. We show in this paper that it is possible to considerably speed ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1207.1512 شماره
صفحات -
تاریخ انتشار 2012