We reformulate branch-and-bound feature selection employing L1 or particular Lp metrics, as mixed-integer linear programming (MILP) problems, affording convenience of widely available MILP solvers. These formulations offer direct influence over individual pairwise interclass margins, which is useful for feature selection in multiclass settings.

In this paper, we introduce an adaptive Lp–norm metric for robust coherent, differential, and noncoherent diversity combining in non–Gaussian noise and interference. We consider the general case where all diversity branches may use different combining weights and different Lp–norms. We derive a general closed–form expression for the asymptotic bit error rate (BER) for Lp–norm combining in indep...

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifica...

In these notes, we review recent results concerning the Lp norm bounds for spectral clusters on compact manifolds. The type of estimates we consider were first established by Sogge [15] in the case of smooth metrics. Recent results of ours in [10] establish the same estimates under the assumption that the metric is C1,1. It is known by examples of Smith-Sogge [12] that such estimates fail for C...

The optimization of investment portfolios is the most important topic in financial decision making, and many relevant models can be found in the literature.  According to importance of portfolio optimization in this paper, deals with novel solution approaches to solve new developed portfolio optimization model. Contrary to previous work, the uncertainty of future retur...

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In this paper, we study performance measures for designing two-band perfect reconstruction (PR) linear phase (LP) filter bank. Based on these performance metrics, we formulate the design problem as a nonlinear constrained optimization problem, where some metrics such as stopband energy have closed form, but the others like transition width do not. Our formulation allows us to search for designs...

The Travelling Salesman Problem is one the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides’s algorithm with approximation factor of 3 2 , even though the so-called HeldKarp LP relaxation of the problem is conjectured to have the integrality gap of only 4 3 . Very recently, signific...

The Travelling Salesman Problem is one of the most fundamental and most studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides’s algorithm with approximation factor of 2 , even though the socalled Held-Karp LP relaxation of the problem is conjectured to have the integrality gap of only 4 3 . Very recently, signifi...