Recognizing conic TDI systems is hard
نویسنده
چکیده
In this note we prove that the problem of deciding whether or not a set of integer vectors forms a Hilbert basis is co-NP-complete. Equivalently, deciding whether a conic linear system is totally dual integral (TDI) or not, is co-NPcomplete. These are true even if the vectors in the set or respectively the coefficient vectors of the inequalities are 0−1 vectors having at most three ones.
منابع مشابه
The complexity of recognizing linear systems with certain integrality properties
Let A be a 0 − 1 matrix with precisely two 1’s in each column and let 1 be the all-one vector. We show that the problems of deciding whether the linear system Ax ≥ 1, x ≥ 0 (1) defines an integral polyhedron, (2) is totally dual integral (TDI), and (3) is box-totally dual integral (box-TDI) are all co-NP-complete, thereby confirming the conjecture on NP-hardness of recognizing TDI systems made ...
متن کاملWEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS
The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...
متن کاملOn Approximate Robust Counterparts of Uncertain Semidefinite and Conic Quadratic Programs
We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic constraints arising in the framework of Robust Convex Programming and demonstrate that these conditions are “tight” up to an absolute constant factor. We discuss applications in Control on the construction of a quadratic Lyapunov function for lin...
متن کاملAutomatically Predicting Sentence Translation Difficulty
In this paper we introduce Translation Difficulty Index (TDI), a measure of difficulty in text translation. We first define and quantify translation difficulty in terms of TDI. We realize that any measure of TDI based on direct input by translators is fraught with subjectivity and adhocism. We, rather, rely on cognitive evidences from eye tracking. TDI is measured as the sum of fixation (gaze) ...
متن کاملRobust Solutions of Uncertain Quadratic and Conic-Quadratic Problems
Abstract. We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when U is given as the intersection of ellipsoids or as an n-dimensional box. For these cases we...
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:
- Math. Program.
دوره 128 شماره
صفحات -
تاریخ انتشار 2011