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The trust region subproblem with a fixed number m additional linear inequality constraints, denoted by (Tm), have drawn much attention recently. The question as to whether Problem (Tm) is in Class P or Class NP remains open. So far, the only affirmative general result is that (T 1) has an exact SOCP/SDP reformulation and thus is polynomially solvable. By(More)
By using the canonical dual transformation developed recently, we derive a pair of canonical dual problems for 0-1 quadratic programming problems in both minimization and maximization form. Regardless convexity, when the canonical duals are solvable, no duality gap exists between the primal and corresponding dual problems. Both global and local optimality(More)
This paper follows the recent discussion on the sparse solution recovery with quasi-norms q, q ∈ (0, 1) when the sensing matrix possesses a Restricted Isometry Constant δ 2k (RIC). Our key tool is an improvement on a version of " the converse of a generalized Cauchy-Schwarz inequality " extended to the setting of quasi-norm. We show that, if δ 2k ≤ 1/2, any(More)