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In this paper, a class of optimization problems is investigated, where the objective function is the sum of N convex functions viewed as local functions and the constraints are N nonidentical closed convex sets. Additionally, it is aimed to solve the considered optimization problem in a distributed manner and thus a sequence of time-varying unbalanced directed graphs is introduced first to depict the information connection topologies. Then, the novel push-sum based constrained optimization algorithm (PSCOA) is developed, where the new gradient descent-like method is applied to settle the involved closed convex set constraints. Furthermore, the rigorous convergence analysis is shown under some standard and common assumptions and it is proved that the developed distributed discrete-time algorithm owns a convergence rate of O ( ln t t ) in general case. Specially, the convergence rate of O ( 1 t ) can be further obtained under the assumption that at least one objective function is strongly convex. Finally, simulation results are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a state-space solution to weight optimization problem in loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified ‘a priori’, thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique. [Copyright &y& Elsevier]

Abstract: This paper proposes a model predictive control (MPC) approach to the periodic implementation of the optimal solutions of a class of resource allocation problems in which the allocation requirements and conditions repeat periodically over time. This special class of resource allocation problems includes many practical energy optimization problems such as load scheduling and generation dispatch. The convergence and robustness of the MPC algorithm is proved by invoking results from convex optimization. To illustrate the practical applications of the MPC algorithm, the energy optimization of a water pumping system is studied. [ABSTRACT FROM AUTHOR]

This paper presents two distributed event-triggered algorithms under directed communication networks to solve a class of convex optimization problems such as the economic dispatch problem (EDP) with equality constraint, while the objective of optimization is the sum of all locally convex functions. One is distributed continuous-time event-triggered optimization algorithm, and the other is discrete-time algorithm based on iteration scheme. Continuous communication is not required by adopting event-triggered communication strategy. It means that the communication cost can be reduced and unnecessary waste of network resources can be avoided. Moreover, the convergence for the proposed algorithms are rigorously proved with the aid of Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, four numerical simulations show the effectiveness and advantages of the two novel distributed event-triggered optimization algorithms. [ABSTRACT FROM AUTHOR]