In this paper, we propose a convex optimization-based algorithm for segmenting myocardial infarct from clinical 2D late-gadolinium enhanced magnetic resonance (LGE-MR) images. Previously segmented left ventricular (LV) myocardium was used to define a region of interest for the infarct segmentation. The infarct segmentation problem was formulated as a continuous min-cut problem, which was solved using its dual formulation, the continuous max-flow (CMF). Bhattacharyya intensity distribution matching was used as the data term, where the prior intensity distributions were computed based on a training data set LGE-MR images from seven patients. The algorithm was parallelized and implemented in a graphics processing unit for reduced computation time. Three-dimensional (3D) volumes of the infarcts were then reconstructed using an interpolation technique we developed based on logarithm of odds. The algorithm was validated using LGE-MR images from 47 patients (309 slices) by comparing computed 2D segmentations and 3D reconstructions to manually generated ones. In addition, the developed algorithm was compared to several previously reported segmentation techniques. The CMF algorithm outperformed the previously reported methods in terms of Dice similarity coefficient.