Convex optimization has provided both a powerful tool and an intriguing mentality to the analysis and design of communication systems over the last few years. A main challenge today is on nonconvex problems in these application. This paper presents an overview of some of the important nonconvex optimization problems in point-to-point and networked communication systems. Three typical applicatio...

This paper introduces to constructing problems of convex relaxations for nonconvex polynomial optimization problems. Branch-and-bound algorithms are convex relaxation based. The convex envelopes are of primary importance since they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulationlinearization technique (RLT) generates LP (linear p...

We present the online Newton's method, a single-step second-order method for nonconvex optimization. analyze its performance and obtain dynamic regret bound that is linear in cumulative variation between round optima. show if optima limited, leads to constant bound. In general case, outperforms convex optimization algorithms functions performs similarly specialized algorithm strongly functions....

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...

  Semidefinite optimization relaxations are among the widely used approaches to find global optimal or approximate solutions for many nonconvex problems. Here, we consider a specific quadratically constrained quadratic problem with an additional linear constraint. We prove that under certain conditions the semidefinite relaxation approach enables us to find a global optimal solution of the unde...

In this paper, we consider a wide class of constrained nonconvex regularized minimization problems, where the constraints are linearly constraints. It was reported in the literature that nonconvex regularization usually yields a solution with more desirable sparse structural properties beyond convex ones. However, it is not easy to obtain the proximal mapping associated with nonconvex regulariz...

This paper presents a comprehensive review and some new developments on canonical duality theory for nonconvex systems. Based on a tri-canonical form for quadratic minimization problems, an insightful relation between canonical dual transformations and nonlinear (or extended) Lagrange multiplier methods is presented. Connections between complementary variational principles in nonconvex mechanic...