A Mathematical Proofs Throughout the following proofs, for the convenience of description, we denote two symbols: the symbol (a,b), which means the angle of two vectors a,b R

Throughout this section, we will assume the same variables as in Eq.1-5 and Section 3 by default, We omit the soft constraints in original objective. "draw the optimal point back" from too far, and thus we can ignore the points outside the When we consider the effect of violating constraints, we only consider non-degraded activated cone, i.e.,, for an activated cone in a Thus it is straightforward to apply our proofs to the general form of Eq.5. A.2 Lemma 7 In order to prove Theorem 2, we give a crucial lemma. Since K is non-degraded, we have r + q n . With equations in Eq. 17, we get See Theorem 3 for the meaning of union.