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Convex optimization aims at searching for the minimum of a convex function over a convex set. While the theory of convex optimization has been largely explored for about a century, several related developments have stimulated a new interest in the topic. The first one is the emergence of efficient optimization algorithms, such as proximal methods, which allow one to easily solve large-size nonsmooth convex problems in a parallel manner. The second development is the discovery of the fact that convex optimization problems are more ubiquitous in practice than was thought previously. In this thesis, we address two different problems within the framework of convex optimization. The first one is an application to computer stereo vision, where the goal is to recover the depth information of a scene from a pair of images taken from the left and right positions. The second one is the proposition of new mathematical tools to deal with convex optimization problems involving information measures, where the objective is to minimize the divergence between two statistical objects such as random variables or probability distributions. We propose a convex approach to address the problem of dense disparity estimation under varying illumination conditions. A convex energy function is derived for jointly estimating the disparity and the illumination variation. The resulting problem is tackled in a set theoretic framework and solved using proximal tools. It is worth emphasizing the ability of this method to process multicomponent images under illumination variation. The conducted experiments indicate that this approach can effectively deal with the local illumination …