Optimization has been widely used in recent design of communication and networking systems. One major hurdle in this endeavor lies in the nonconvexity of many optimization problems that arise from practical systems. To address this issue, we observe that most nonconvex problems encountered in communication and networking systems exhibit monotonicity or hidden monotonicity structures. A systematic use of the monotonicity properties would substantially alleviate the difficulty in obtaining the global optimal solutions of the problems. This monograph provides a succinct and accessible introduction to monotonic optimization, including the formulation skills and solution algorithms. Through several application examples, we will illustrate modeling techniques and algorithm details of monotonic optimization in various scenarios. With this promising technique, many previously difficult problems can now be solved with great efficiency. With this monograph, we wish to spur new research activities in broadening the scope of application of monotonic optimization in communication and networking systems.

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Future smart grid (SG) has been considered a complex and advanced power system, where energy consumers are connected not only to the traditional energy retailers (e.g., the utility companies) but also to some local energy networks for bidirectional energy trading opportunities. This paper aims to investigate a hybrid energy trading market that is comprised of an external utility company and a local trading market managed by a local trading center (LTC). The existence of local energy market provides new opportunities for the energy consumers and the distributed energy sellers to perform the local energy trading in a cooperative manner such that they all can benefit. This paper first quantifies the respective benefits of the energy consumers and the sellers from the local trading and then investigates how they can optimize their benefits by controlling their energy scheduling, in response to the LTC's pricing. Two different types of the LTC are considered, i.e., i) the nonprofit-oriented LTC which solely aims at benefiting the energy consumers and the sellers, and ii) the profit-oriented LTC which aims at maximizing its own profit while guaranteeing the required benefit for each consumer and seller. For each type of the LTC, the optimal trading problem is formulated and the associated algorithm is further proposed to efficiently find the LTC's optimal price as well as the optimal energy scheduling for each consumer and seller. Numerical results are provided to validate the benefits of the hybrid energy trading market and the performance of the proposed algorithms.

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