Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of Censor and Elfving for solving the CFP,...

Abstract The current bottleneck of globally solving mixed-integer (nonconvex) quadratically constrained problems (MIQCPs) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are present. We propose a cutting-surface method based on multiple diagonal perturbations to derive convex quadratic relaxations for nonconvex quadratic probl...

This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial optimization problems in the face of data uncertainty. The class of convex optimization problems, called robust SOS-convex polynomial optimization problems, includes robust quadratically constrained convex optimization problems and robust separable convex polynomial optimiza...

In this paper we study the multiple input multiple output (MIMO) orthogonal freqency division multiplexing (OFDM) Gaussian Broadcast Channel (BC). Several fundamental problems are considered: The maximization of a weighted sum of rates and the dual minimization of sum power subject to rate requirements. Further we study the combined problem of weighted rate sum maximization under minimum rate r...

In this lecture, we discuss first order methods for the minimization of convex functions. We focus almost exclusively on subgradient-based methods, which are essentially universally applicable for convex optimization problems, because they rely very little on the structure of the problem being solved. This leads to effective but slow algorithms in classical optimization problems, however, in la...

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function f : X×Y → R is called biconvex, if f(x, y) is convex in y for fixed x ∈ X, and f(x, y) is convex in x for fixed y ∈ Y . This paper presents a ...

Unmanned aerial vehicles (UAVs) have steadily gained attention to overcome the harsh propagation loss and blockage issue of millimeter-wave communication. However, UAV communication systems suffer from energy consumption, which limits flying time UAVs. In this paper, we propose several consumption minimization techniques through aid multiple intelligent reflecting surfaces (IRSs). specific, int...