Rejoinder of “ Hypothesis testing by convex optimization ” ∗

Rejoinder: Latent Variable Graphical Model Selection via Convex Optimization by Venkat Chandrasekaran,

Hypothesis testing by convex optimization

We discuss a general approach to hypothesis testing. The main “building block” of the proposed construction is a test for a pair of hypotheses in the situation where each particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated with the hypothesis. This test, under appropriate assumptions, is nearly optima...

Comment on “ Hypothesis testing by convex optimization ” ∗

With the growing size of problems at hand, convexity has become preponderant in modern statistics. Indeed, convex relaxations of NP-hard problems have been successfully employed in a variety of statistical problems such as classification [2, 16], linear regression [7, 5], matrix estimation [8, 12], graphical models [15, 9] or sparse principal component analysis (PCA) [10, 4]. The paper “Hypothe...

On Sequential Hypotheses Testing via Convex Optimization

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solutio...

Linear Time Varying MPC Based Path Planning of an Autonomous Vehicle via Convex Optimization

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...