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...

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orthogonality constraint. Convex sparsity-inducing ...

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly constrained nonconvex problems. For optimization problems of the above structure, we propose random ...

A nonconvex optimization algorithm is developed, which exploits gradient magnitude image (GMI) sparsity for reduction in the projection view angle sampling rate. The algorithm shows greater potential for exploiting GMI sparsity than can be obtained by convex total variation (TV) based optimization. The nonconvex algorithm is demonstrated in simulation with ideal, noiseless data for a 2D fan-bea...

A branch and bound global optimization method, BB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bil...

In this paper we study the lq-analysis optimization (0 < q ≤ 1) problem for cosparse signal recovery. Our results show that the nonconvex lq-analysis optimization with q < 1 has better properties in terms of stability and robustness than the convex l1-analysis optimization. In addition, we develop an iteratively reweighted method to solve this problem under the variational framework. Theoretica...