Successive Convex Approximations to Cardinality-Constrained Convex Programs: A Piecewise-Linear DC Approach

In this paper we consider cardinality-constrained convex programs that minimize a convex function subject to a cardinality constraint and other linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality function is first approximated by a piecewise linear DC function (difference of two convexfunctions) and a sequence of convex subproblems is then constructed by successively linearizing the concave terms of the DC function. Under some mild assumptions, we establish that any accumulation point of the sequence generated by the method is a KKT point of the DC approximation problem. We show that the basic algorithm can be refined by adding strengthening cuts in the subproblems. Finally, we report some preliminary computational results on cardinality-constrained portfolio selection problems

Determination of the number of J/ψ events with inclusive J/ψ decays

A measurement of the number of J/ψ events collected with the BESIII detector in 2009 and 2012 is performed using inclusive decays of the J/ψ. The number of J/ψ events taken in 2009 is recalculated to be (223.7 ± 1.4) × 106, which is in good agreement with the previous measurement, but with significantly improved precision due to improvements in the BESIII software. The number of J/ψ events taken in 2012 is determined to be (1086.9 ± 6.0) × 106. In total, the number of J/ψ events collected with the BESIII detector is measured to be (1310.6 ± 7.0) × 106, where the uncertainty is dominated by systematic effects and the statistical uncertainty is negligible

Measurements of the center-of-mass energies at BESIII via the di-muon process

From 2011 to 2014, the BESIII experiment collected about 5 fb-1 data at center-of-mass energies around 4 GeV for the studies of the charmonium-like and higher excited charmonium states. By analyzing the di-muon process e+e- → γISR/FSRμ+μ-, the center-of-mass energies of the data samples are measured with a precision of 0.8 MeV. The center-of-mass energy is found to be stable for most of the time during data taking