It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/T~(1/2)), which is same as stochastic optimization of Lips-chitz continuous convex functions. This is in contra...
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ISBN:
(纸本)9781632660244
It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/T~(1/2)), which is same as stochastic optimization of Lips-chitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence rate of O(1/T~2). In this work, we consider a new setup for optimizing smooth functions, termed as Mixed optimization, which allows to access both a stochastic oracle and a full gradient oracle. Our goal is to significantly improve the convergence rate of stochastic optimization of smooth functions by having an additional small number of accesses to the full gradient oracle. We show that, with an O(ln T) calls to the full gradient oracle and an O(T) calls to the stochastic oracle, the proposed mixed optimization algorithm is able to achieve an optimization error of O(1/T).
Protecting infrastructures against natural hazards is a pressing national and international problem. Given the current budgetary climate, the ability to determine the best mitigation strategies with highly constrained...
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ISBN:
(纸本)9781479920778
Protecting infrastructures against natural hazards is a pressing national and international problem. Given the current budgetary climate, the ability to determine the best mitigation strategies with highly constrained budgets is essential. This papers describes a set of computationally efficient techniques to determine optimal infrastructure investment strategies, given multiple user objectives, that are consistent with an underlying earthquake hazard. These techniques include: optimization methods for developing representative events to characterize the hazard and the post-event condition of infrastructure components, a simulation model to characterize post-event infrastructure performance relative to multiple user objectives, and a multi-objective optimization algorithm for determining protection strategies. They are demonstrated using a case study of the highway network in Memphis, Tennessee.
In order to solve the problem of satellite moving interference location, a localization algorithm based on search optimization for dual satellite systems is presented. By using the measurements of the TDOA/FDOA and th...
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ISBN:
(纸本)9781479927654
In order to solve the problem of satellite moving interference location, a localization algorithm based on search optimization for dual satellite systems is presented. By using the measurements of the TDOA/FDOA and the Doppler frequency of the moving interfering transmitter, the position of the moving interference can be located in the point of intersection of the curved surface of TDOA/FDOA and the Doppler frequency theoretically. Simulation results verify the effectiveness of the proposed algorithm.
Many real-world problems have complicated objective functions. To optimize such functions, humans utilize sophisticated sequential decision-making strategies. Many optimization algorithms have also been developed for ...
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ISBN:
(纸本)9781632660244
Many real-world problems have complicated objective functions. To optimize such functions, humans utilize sophisticated sequential decision-making strategies. Many optimization algorithms have also been developed for this same purpose, but how do they compare to humans in terms of both performance and behavior? We try to unravel the general underlying algorithm people may be using while searching for the maximum of an invisible 1D function. Subjects click on a blank screen and are shown the ordinate of the function at each clicked abscissa location. Their task is to find the function's maximum in as few clicks as possible. Subjects win if they get close enough to the maximum location. Analysis over 23 non-maths undergraduates, optimizing 25 functions from different families, shows that humans outperform 24 well-known optimization algorithms. Bayesian optimization based on Gaussian Processes, which exploits all the x values tried and all the f(x) values obtained so far to pick the next x, predicts human performance and searched locations better. In 6 follow-up controlled experiments over 76 subjects, covering interpolation, extrapolation, and optimization tasks, we further confirm that Gaussian Processes provide a general and unified theoretical account to explain passive and active function learning and search in humans.
This paper considers the computation time of two algorithms for solving a structured constrained linear optimal control problem with finite horizon quadratic cost within the context of automated irrigation networks. T...
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ISBN:
(纸本)9781467357159
This paper considers the computation time of two algorithms for solving a structured constrained linear optimal control problem with finite horizon quadratic cost within the context of automated irrigation networks. The first is a standard centralized algorithm based on the interior point method that does not exploit problem structure. The second is distributed and based on a consensus algorithm, not specifically tailored to account for system structure, but devised rather to facilitate the management of conflicting computational and communication overheads. It is shown that there is a significant advantage in terms of computation time in using the second algorithm in large-scale networks. Specifically, for a fixed horizon length the computation time of the centralized algorithm grows as O(n~4) with the number n of sub-systems. By contrast, it is observed via a combination of analysis and experiment that the computation time of the distributed algorithm grows as O(n) with the number n of sub-systems.
A massive number of distributed energy resources (DER), battery energy storage systems (BESS), and smart appliances (loads) is expected to be deployed in the future. To capture the benefits associated with these emerg...
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ISBN:
(纸本)9781479912537
A massive number of distributed energy resources (DER), battery energy storage systems (BESS), and smart appliances (loads) is expected to be deployed in the future. To capture the benefits associated with these emerging units, this paper proposes an advanced infrastructure that allows for an accurate and fast monitoring of the distribution electric feeder including various types of residential, commercial, and industrial loads. This scheme allows for optimizing the utilization and operation of the power system over a short term planning period. More precisely, the concept of distributed optimization algorithm through decomposing the problem into small parts is used to achieve the outlined goals. The enabling technologies that facilitate the implementation of the proposed infrastructure are the advanced metering devices and the distributed state estimation (DSE). The meters, basically, gather the system synchronized and non-synchronized data and send them to the DSE, which evaluates the real time model of the system 60 times per seconds. The results of the DSE are used to perform the optimization and set the controls for the system autonomously.
An important challenge in multiagent systems is consensus, in which the agents must agree on certain controlled variables of interest. So far, most consensus algorithms for agents with nonlinear dynamics exploit the s...
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ISBN:
(纸本)9781467357159
An important challenge in multiagent systems is consensus, in which the agents must agree on certain controlled variables of interest. So far, most consensus algorithms for agents with nonlinear dynamics exploit the specific form of the nonlinearity. Here, we propose an approach that only requires a black-box simulation model of the dynamics, and is therefore applicable to a wide class of nonlinearities. This approach works for agents communicating on a fixed, connected network. It designs a reference behavior with a classical consensus protocol, and then finds control actions that drive the nonlinear agents towards the reference states, using a recent optimistic optimization algorithm. By exploiting the guarantees of optimistic optimization, we prove that the agents achieve practical consensus. A representative example is further analyzed, and simulation results on nonlinear robotic arms are provided.
The aim of the optimal safety controller synthesis problem is to synthesize a feedback controller that results in closed-loop trajectories that meet certain criteria, namely, the state or output trajectories terminate...
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ISBN:
(纸本)9781479901777
The aim of the optimal safety controller synthesis problem is to synthesize a feedback controller that results in closed-loop trajectories that meet certain criteria, namely, the state or output trajectories terminate in a goal set without entering an unsafe set while optimizing some function. Our previous work presented a method for using finitely many human generated trajectories to synthesize a non-optimal safety controller. We propose a formal method for optimizing the human generated trajectories used to synthesize the controller. Our method is based on the calculus of variations, but is different from other similar algorithms in that it uses a gradient descent based approach to directly solve the optimization problem without formulating the optimality conditions given by the Pontryagin Minimum Principle. This method provides a tool for improving the performance of a controller synthesized using the methods outlined in our previous work. We present an example of optimizing a human generated trajectory for a nonlinear system, specifically a quadrotor, and quantify the improvements it is able to generate.
We discuss a multiplicative update quadratic programming algorithm with applications to model predictive control for constrained linear systems. The algorithm, named PQP, is very simple to implement and thus verify, d...
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ISBN:
(纸本)9781467357159
We discuss a multiplicative update quadratic programming algorithm with applications to model predictive control for constrained linear systems. The algorithm, named PQP, is very simple to implement and thus verify, does not require projection, offers a linear rate of convergence, and can be completely parallelized. The PQP algorithm is equipped with conditions that guarantee the desired bound on suboptimality and with an acceleration step based on projection-free line search. We also show how PQP can take advantage of the parametric structure of the MPC problem, thus moving offline several calculations and avoiding large input/output dataflows. The algorithm is evaluated on two benchmark problems, where it is shown to compete with, and possibly outperform, other open source and commercial packages.
The use of multiple optimization algorithms to solve a design problem in electromagnetics can offer more reliable runs and further ensure robustness in finding the global optimum design. Utilizing multiple techniques ...
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ISBN:
(纸本)9781467353168
The use of multiple optimization algorithms to solve a design problem in electromagnetics can offer more reliable runs and further ensure robustness in finding the global optimum design. Utilizing multiple techniques can more thoroughly search the solution space, and the advantages of each algorithm can be exploited. The PSO and CMA-ES techniques are selected to demonstrate this due to the substantial differences in their exploration mechanisms in multi-dimensional spaces. These techniques are applied to mathematical benchmark functions as well as a stacked patch design for use in weather radar systems.
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