This paper addresses the problem of data-adaptive learning of the ambient geometry of a nonlinear, non-intersecting submanifold of a Euclidean space. It accomplishes this goal by exploiting the local linearity of the (sub)manifold and approximating it using a union of tangent patches (UoTP). In addition, it translates the problem of projecting a new data point onto the learned UoTP into a serie...

Accurate nonlinear dynamic models of process operations such as start-ups, shut-downs, and complex changeovers include state dependent events that trigger discrete changes to the describing equations, and are best analyzed within a hybrid systems framework. The automated design of an optimal process operation can thus be formulated as a dynamic optimization problem with a hybrid system embedded...

Consider a minimization problem given by a nonlinear, convex objective function over a nonconvex feasible region. Traditional optimization approaches will frequently encounter a fundamental difficulty when dealing with such problems: even if we can efficiently optimize over the convex hull of the feasible region, the optimum will likely lie in the interior of a high dimensional face, “far away”...

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...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite ...

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative appr...