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12
Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods
, 2007
"... We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the met ..."
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Cited by 79 (7 self)
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We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradient iterations increases to infinity). Furthermore, no convergence rate results are known for these algorithms. In this paper, we propose and analyze dual subgradient methods using averaging to generate approximate primal optimal solutions. These algorithms use a constant stepsize as opposed to a diminishing stepsize which is dominantly used in the existing primal recovery schemes. We provide estimates on the convergence rate of the primal sequences. In particular, we provide bounds on the amount of feasibility violation of the generated approximate primal solutions. We also provide upper and lower bounds on the primal function values at the approximate solutions. The feasibility violation and primal value estimates are given per iteration, thus providing practical stopping criteria. Our analysis relies on the Slater condition and the inherited boundedness properties of the dual problem under this condition.
Temperature-aware scheduling and assignment for hard real-time applications on MPSoCs
, 2010
"... Increasing integrated circuit (IC) power densities and temperatures may hamper multiprocessor system-on-chip (MPSoC) use in hard real-time systems. This article formalizes the temperature-aware real-time MPSoC assignment and scheduling problem and presents an optimal phased steadystate mixed intege ..."
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Cited by 42 (1 self)
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Increasing integrated circuit (IC) power densities and temperatures may hamper multiprocessor system-on-chip (MPSoC) use in hard real-time systems. This article formalizes the temperature-aware real-time MPSoC assignment and scheduling problem and presents an optimal phased steadystate mixed integer linear programming based solution that considers the impact of scheduling and assignment decisions on MPSoC thermal profiles to directly minimize the chip peak temperature. We also introduce a flexible heuristic framework for task assignment and scheduling that permits system designers to trade off accuracy for running time when solving large problem instances. Finally, for task sets with sufficient slack, we show that inserting idle times between task executions can further reduce the peak temperature of the MPSoC quite significantly.
Code generation for receding horizon control
- In Proceedings of the IEEE International Symposium on Computer-Aided Control System Design
, 2010
"... Abstract — Receding horizon control (RHC), also known as model predictive control (MPC), is a general purpose control scheme that involves repeatedly solving a constrained optimization problem, using predictions of future costs, disturbances, and constraints over a moving time horizon to choose the ..."
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Cited by 11 (4 self)
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Abstract — Receding horizon control (RHC), also known as model predictive control (MPC), is a general purpose control scheme that involves repeatedly solving a constrained optimization problem, using predictions of future costs, disturbances, and constraints over a moving time horizon to choose the control action. RHC handles constraints, such as limits on control variables, in a direct and natural way, and generates sophisticated feed-forward actions. The main disadvantage of RHC is that an optimization problem has to be solved at each step, which leads many control engineers to think that it can only be used for systems with slow sampling (say, less than one Hz). Several techniques have recently been developed to get around this problem. In one approach, called explicit MPC, the optimization problem is solved analytically and explicitly, so evaluating the control policy requires only a lookup table search. Another approach, which is our focus here, is to exploit the structure in the optimization problem to solve it efficiently. This approach has previously been applied in several specific cases, using custom, hand written code. However, this requires significant development time, and specialist knowledge of optimization and numerical algorithms. Recent developments in convex optimization code generation have made the task much easier and quicker. With code generation, the RHC policy is specified in a high-level language, then automatically transformed into source code for a custom solver. The custom solver is typically orders of magnitude faster than a generic solver, solving in milliseconds or microseconds on standard processors, making it possible to use RHC policies at kilohertz rates. In this paper we demonstrate code generation with two simple control examples. They show a range of problems that may be handled by RHC. In every case, we show a speedup of several hundred times from generic parser-solvers. I.
A Cyber-Physical Systems Approach to Data Center Modeling and Control for Energy Efficiency
"... Abstract—This paper presents data centers from a cyberphysical system (CPS) perspective. Current methods for controlling information technology (IT) and cooling technology (CT) in data centers are classified according to the degree to which they take into account both cyber and physical consideratio ..."
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Cited by 5 (1 self)
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Abstract—This paper presents data centers from a cyberphysical system (CPS) perspective. Current methods for controlling information technology (IT) and cooling technology (CT) in data centers are classified according to the degree to which they take into account both cyber and physical considerations. To evaluate the potential impact of coordinated CPS strategies at the data-center level, we introduce a control-oriented model that represents the data center as two coupled networks: a computational network representing the cyber dynamics and a thermal network representing the physical dynamics. These networks are coupled through the influence of the IT on both networks: servers affect both the quality of service (QoS) delivered by the computational network and the generation of heat in the thermal network. Using this model, three control strategies are evaluated with respect to their energy efficiency and computational performance: a baseline strategy that ignores CPS considerations, an uncoordinated strategy that manages the IT and CT independently, and a coordinated strategy that manages the IT and CT together to achieve optimal performance with respect to both QoS and energy efficiency. Simulation results show that the benefits to be realized from coordinating the control of IT and CT depend on the distribution and heterogeneity of the computational and cooling resources throughout the data center. A new cyber-physical index (CPI) is introduced as a measure of this combined distribution of cyber and physical effects in a given data center. We illustrate how the CPI indicates the potential impact of using coordinated CPS control strategies.
Robust Optimization of a Chip Multiprocessor's Performance under Power and Thermal Constraints
- in International Conference in Computer Design (ICCD
, 2012
"... Abstract – Power dissipation and die temperature have become key performance limiters in today’s high-performance Chip Multiprocessors (CMPs.) Dynamic power management solutions have been proposed to manage resources in a CMP based on the measured power dissipation, performance, and die temperature ..."
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Cited by 2 (1 self)
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Abstract – Power dissipation and die temperature have become key performance limiters in today’s high-performance Chip Multiprocessors (CMPs.) Dynamic power management solutions have been proposed to manage resources in a CMP based on the measured power dissipation, performance, and die temperature of processing cores. In this paper, we develop a robust framework for power and thermal management of heterogeneous CMPs subject to variability and uncertainty in system parameters. More precisely, we first model and formulate the problem of maximizing the task throughput of a heterogeneous CMP (a.k.a., asymmetric multi-core architecture) subject to a total power budget and a per-core temperature limit. Next we develop a solution framework, called Variation-aware Power/Thermal Manager (VPTM), which is a hierarchical dynamic power and thermal management solution targeting heterogeneous CMP architectures. VPTM utilizes dynamic voltage and frequency scaling (DVFS) and core consolidation techniques to control the core power consumptions, which implicitly regulate the core temperatures. An algorithm is proposed for core consolidation and application assignment, and a convex program is formulated and solved to produce optimal DVFS settings. Finally, a feedback controller is employed to compensate for variations in key system parameters at runtime. Experimental results show highly promising performance improvements for VPTM compared to the stateof-the-art techniques. I.
User-Centric Energy-Efficient Scheduling on Multi-Core Mobile Devices
"... Mobile devices will provide improved computing resources to sustain progressively more complicated applications. However, the design concept of fair scheduling and governing borrowed from legacy operating systems cannot be applied seamlessly in mobile systems, thereby degrading user experience or re ..."
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Cited by 1 (0 self)
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Mobile devices will provide improved computing resources to sustain progressively more complicated applications. However, the design concept of fair scheduling and governing borrowed from legacy operating systems cannot be applied seamlessly in mobile systems, thereby degrading user experience or reducing energy efficiency. In this paper, we posit that mobile applica-tions should be treated unfairly. To this end, we exploit the con-cept of application sensitivity and devise a user-centric scheduler and governor that allocate computing resources to applications according to their sensitivity. Furthermore, we integrate our design into the Android operating system. The results of exten-sive experiments on a commercial smartphone with real-world mobile apps demonstrate that the proposed design can achieve significant energy efficiency gains while improving the quality of user experience.
Models and Control Strategies for Data Center Energy Efficiency
"... As the foundation of the nation’s information infrastructure, data centers have been growing rapidly in both number and capacity to meet the increasing demands for highlyresponsive computing and massive storage. Data center energy consumption doubled from 2000 to 2006, reaching a value of 60 TWh/yea ..."
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As the foundation of the nation’s information infrastructure, data centers have been growing rapidly in both number and capacity to meet the increasing demands for highlyresponsive computing and massive storage. Data center energy consumption doubled from 2000 to 2006, reaching a value of 60 TWh/year (Tera Watt hour / year). Coupled with increasing power and cooling demands imposed by the Moore’s law and with the quest for high density data centers, this trend has been rapidly raising the energy cost associated with data centers. Data centers are large cyber-physical systems (CPSs) with hundreds of variables that can be measured and controlled. Dynamics of the controlled processes span multiple time scales: electricity costs can fluctuate hourly, temperatures evolve in the order of minutes, and CPU power states can be changed as frequent as milliseconds. Processes also differ in the spatial areas they influence: computer room air conditioners (CRAC) affect the inlet air temperatures of multiple servers, whereas CPU power states affect only single servers. The large number of constraints and their heterogeneity in nature make data center control
JACOB MATTINGLEY,
"... Receding horizon control (RHC), also known as model predictive control (MPC), [1]–[5] is a feedback control technique that became popular in the 1980s. With RHC, an optimization problem is solved at each time step to determine a plan of action over a fixed time horizon. The first input from this pla ..."
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Receding horizon control (RHC), also known as model predictive control (MPC), [1]–[5] is a feedback control technique that became popular in the 1980s. With RHC, an optimization problem is solved at each time step to determine a plan of action over a fixed time horizon. The first input from this plan is applied to the system. At the next time step we repeat the planning process, solving a new optimization problem with the time horizon shifted one step forward. The optimization problem takes into account estimates of future quantities based on available information at each time step. The control policy involves feedback since real-time measurements are used to determine the control input.
