What is convexification?

A globally convergent (the so-called convexification) algorithm was developed for coefficient inverse problems (CIPs) with time/frequency-dependent data. Convexification is extended to the case of a CIP for an elliptic equation with data generated by the source, running along a straight line. The data are incomplete, since they are given only at a part of the boundary. Applications to electrical impedance and optical tomographies are feasible, particularly in imaging of landmines and underground bunkers as well as diffuse optical imaging of targets on battlefields through smogs and flames.