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A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we show that the natural temporal variation may help simple online tracking methods find and track time-varying global minima. To this end, we investigate the properties of a time-varying projected gradient flow system with inertia, which can be regarded as the continuous-time limit of (1) the optimality conditions for a discretized sequential optimization problem with a proximal regularization and (2) the online tracking scheme. We introduce the notion of the dominant trajectory and show that the inherent temporal variation could re-shape the landscape of the Lagrange functional and help a proximal algorithm escape the spurious local minimum trajectories if the global minimum trajectory is dominant. For a problem with twice continuously differentiable objective function and constraints, sufficient conditions are derived to guarantee that no matter how a local search method is initialized, it will track a time-varying global solution after some time. The results are illustrated on a benchmark example with many local minima.
This paper considers a time-varying optimization problem associated with a network of systems, with each of the systems shared by (and affecting) a number of individuals. The objective is to minimize cost functions associated with the individuals pre
Distributed optimization is concerned with using local computation and communication to realize a global aim of optimizing the sum of local objective functions. It has gained wide attention for a variety of applications in networked systems. This pap
There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), d
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We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for th