In this paper we study general lp regularized unconstrained matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them. And we show that the first-order stationary points introduced in [11] for an lp regularized vector minimization problem are equivalent to those of an lp regularized matrix minimization reformulation. We also establish that...

This note gives proves two theorems. The first is that it is consistent to have ωn for every n, but not have אω . This is done by carefully collapsing a supercompact cardinal and adding square sequences to each ωn. The crux of the proof is that in the resulting model every stationary subset of אω+1∩cof(ω) reflects to an ordinal of cofinality ω1, that is to say it has stationary intersection wit...

In this paper we study general Schatten-p quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized vector minimization problem are equivalent to those of an SPQN regularized matrix minimization reformulation. We also s...

We prove a number of consistency results complementary to the ZFC results from our paper [4]. We produce examples of non-tightly stationary mutually stationary sequences, sequences of cardinals on which every sequence of sets is mutually stationary, and mutually stationary sequences not concentrating on a fixed cofinality. We also give an alternative proof for the consistency of the existence o...

this paper presents a new formulation for warehouse inventory management in a stochastic situation. the primary source of this formulation is derived from fp model, which has been proposed by fletcher and ponnambalam for reservoir management. the new proposed mathematical model is based on the first and the second moments of storage as a stochastic variable. using this model, the expected value...