A simple effective heuristic for embedded mixed-integer quadratic programming

In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimization problems. We discuss the favorable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we find that in many cases, it finds the global solution

Generalisation of code division multiple access systems and derivation of new bounds for the sum capacity

In this study, the authors explore a generalised scheme for the synchronous code division multiple access (CDMA). In this scheme, unlike the standard CDMA systems, each user has different codewords for communicating different messages. Two main problems are investigated. The first problem concerns whether uniquely detectable overloaded matrices (an injective matrix, i.e. the inputs and outputs are in one-to-one correspondence depending on the input alphabets) exist in the absence of additive noise, and if so, whether there are any practical optimum detectors for such input codewords. The second problem is about finding tight bounds for the sum channel capacity. In response to the first problem, the authors have constructed uniquely detectable matrices for the generalised scheme and the authors have developed practical maximum likelihood detection algorithms for such codes. In response to the second problem, lower bounds and conjectured upper bounds are derived. The results of this study are superior to other standard overloaded CDMA codes since the generalisation can support more users than the previous schemes