scholarly journals Real-time Bidding for Time Constrained Impression Contracts in First and Second Price Auctions - Theory and Algorithms

2021 ◽  
Vol 5 (3) ◽  
pp. 1-37
Author(s):  
Ryan J. Kinnear ◽  
Ravi R. Mazumdar ◽  
Peter Marbach
Keyword(s):  
Real Time ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Piecewise Constant Function ◽  
Convex Optimization Problem ◽  
Piecewise Constant ◽  
Infinite Dimensional ◽  
Optimal Behavior ◽  
Price Auction ◽  
Second Price Auctions

We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.

Design of Low Order Controllers for Decoupled MIMO Systems With Time Response Specifications

2018 ◽  
pp. 90-128
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Mimo Systems ◽  
Design Method ◽  
Optimal Solution ◽  
Time Response ◽  
Convex Optimization Problem ◽  
Tito Systems ◽  
Low Order

The design of a low order controller for decoupled MIMO systems is proposed. The main objective of this controller is to guarantee some closed loop time response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a non-convex optimization problem. In order to obtain an optimal solution, the use of a global optimization method is suggested. In this chapter, the proposed solution is the GGP method. The principle of this method consists of transforming a non-convex optimization problem to a convex one by some mathematical transformations. So as to accomplish the fixed goal, it is imperative to decouple the coupled MIMO systems. To approve the controllers' design method, the synthesis of fixed low order controller for decoupled TITO systems is presented firstly. Then, this design method is generalized in the case of MIMO systems. Simulation results and a comparison study between the presented approach and a PI controller are given in order to show the efficiency of the proposed controller. It is remarkable that the obtained solution meets the desired closed loop time specifications for each system output. It is also noted that by considering the proposed approach the user can fix the desired closed loop performances for each output independently.

A variational approach to nonlinear stochastic differential equations with linear multiplicative noise

2019 ◽  
Vol 25 ◽  
pp. 71
Author(s):  
Viorel Barbu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Parabolic Equations ◽  
Optimization Problem ◽  
Multiplicative Noise ◽  
Generalized Solution ◽  
Convex Optimization Problem ◽  
Nonlinear Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Wiener Processes

One introduces a new concept of generalized solution for nonlinear infinite dimensional stochastic differential equations of subgradient type driven by linear multiplicative Wiener processes. This is defined as solution of a stochastic convex optimization problem derived from the Brezis-Ekeland variational principle. Under specific conditions on nonlinearity, one proves the existence and uniqueness of a variational solution which is also a strong solution in some significant situations. Applications to the existence of stochastic total variational flow and to stochastic parabolic equations with mild nonlinearity are given.

scholarly journals Minimizing Power Consumption of an Experimental HVAC System Based on Parallel Grid Searching

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2083 ◽  
Author(s):  
Wangqi Xiong ◽  
Jiandong Wang
Keyword(s):  
Power Consumption ◽  
Graphics Processing Units ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Hvac System ◽  
Convex Optimization Problem ◽  
The One ◽  
Graphics Processing

This paper proposes a parallel grid search algorithm to find an optimal operating point for minimizing the power consumption of an experimental heating, ventilating and air conditioning (HVAC) system. First, a multidimensional, nonlinear and non-convex optimization problem subject to constraints is formulated based on a semi-physical model of the experimental HVAC system. Second, the optimization problem is parallelized based on Graphics Processing Units to simultaneously compute optimization loss functions for different solutions in a searching grid, and to find the optimal solution as the one having the minimum loss function. The proposed algorithm has an advantage that the optimal solution is known with evidence as to the best one subject to current resolutions of the searching grid. Experimental studies are provided to support the proposed algorithm.

scholarly journals Sensitivity functionals in convex optimization problem

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3681-3687
Author(s):  
Robert Namm ◽  
Gyungsoo Woo
Keyword(s):  
Variational Inequality ◽  
Convex Optimization ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Convex Optimization Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional

We consider sensitivity functionals and Lagrange multiplier method for solving finite dimensional convex optimization problem.An analysis based on this property is also applied for semicoercive infinite dimensional variational inequality in mechanics.

scholarly journals INDIVIDUAL LEARNING ABOUT CONSUMPTION

2001 ◽  
Vol 5 (02) ◽  
pp. 255-271 ◽  
Author(s):  
Todd W. Allen ◽  
Christopher D. Carroll
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Individual Learning ◽  
Household Behavior ◽  
Trial And Error ◽  
Optimal Behavior ◽  
Stochastic Optimization Problem ◽  
Rules Of Thumb ◽  
Dynamic Stochastic ◽  
Consumption Saving

The standard approach to modeling consumption/saving problems is to assume that the decisionmaker is solving a dynamic stochastic optimization problem. However, under realistic descriptions of utility and uncertainty, the optimal consumption/saving decision is so difficult that only recently have economists managed to find solutions, using numerical methods that require previously infeasible amounts of computation. Yet, empirical evidence suggests that household behavior conforms fairly well with the prescriptions of the optimal solution, raising the question of how average households can solve problems that economists, until recently, could not. This paper examines whether consumers might be able to find a reasonably good rule-of-thumb approximation to optimal behavior by trial-and-error methods, as Milton Friedman proposed long ago. We find that such individual learning methods can reliably identify reasonably good rules of thumb only if the consumer is able to spend absurdly large amounts of time searching for a good rule.

scholarly journals Data Rate Maximization in RIS-Assisted D2D Communication with Transceiver Hardware Impairments

Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Hongxia Zheng ◽  
Chiya Zhang ◽  
Yatao Yang ◽  
Xingquan Li ◽  
Chunlong He
Keyword(s):  
Optimization Problem ◽  
Original Problem ◽  
Optimal Solution ◽  
Base Station ◽  
D2d Communication ◽  
Convex Optimization Problem ◽  
Hardware Impairments ◽  
Convex Problems ◽  
Rate Maximization ◽  
Power Limit

We maximize the transmit rate of device-to-device (D2D) in a reconfigurable intelligent surface (RIS) assisted D2D communication system by satisfying the unit-modulus constraints of reflectin elements, the transmit power limit of base station (BS) and the transmitter in a D2D pair. Since it is a non-convex optimization problem, the block coordinate descent (BCD) technique is adopted to decouple this problem into three subproblems. Then, the non-convex subproblems are approximated into convex problems by using successive convex approximation (SCA) and penalty convex-concave procedure (CCP) techniques. Finally, the optimal solution of original problem is obtained by iteratively optimizing the subproblems. Simulation results reveal the validity of the algorithm that we proposed to solve the optimization problem and illustrate the effectiveness of RIS to improve the transmit rate of the D2D pair even with hardware impairments.

Real-time recognition of team behaviors by multisensory graph-embedded robot learning

2021 ◽  
pp. 027836492110431
Author(s):  
Brian Reily ◽  
Peng Gao ◽  
Fei Han ◽  
Hua Wang ◽  
Hao Zhang
Keyword(s):  
Real Time ◽  
Latent Variables ◽  
Optimization Problem ◽  
Autonomous Robots ◽  
Critical Role ◽  
Optimal Solution ◽  
Representation Learning ◽  
Robot Learning ◽  
Intent Recognition ◽  
Regularized Optimization

Awareness of team behaviors (e.g., individual activities and team intents) plays a critical role in human–robot teaming. Autonomous robots need to be aware of the overall intent of the team they are collaborating with in order to effectively aid their human peers or augment the team’s capabilities. Team intents encode the goal of the team, which cannot be simply identified from a collection of individual activities. Instead, teammate relationships must also be encoded for team intent recognition. In this article, we introduce a novel representation learning approach to recognizing team intent awareness in real-time, based upon both individual human activities and the relationship between human peers in the team. Our approach formulates the task of robot learning for team intent recognition as a joint regularized optimization problem, which encodes individual activities as latent variables and represents teammate relationships through graph embedding. In addition, we design a new algorithm to efficiently solve the formulated regularized optimization problem, which possesses a theoretical guarantee to converge to the optimal solution. To evaluate our approach’s performance on team intent recognition, we test our approach on a public benchmark group activity dataset and a multisensory underground search and rescue team behavior dataset newly collected from robots in an underground environment, as well as perform a proof-of-concept case study on a physical robot. The experimental results have demonstrated both the superior accuracy of our proposed approach and its suitability for real-time applications on mobile robots.

scholarly journals Energy Efficiency Maximization with Optimal Beamforming in Secure MISO CRNs with SWIPT

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Liang Xue ◽  
Yao Ma ◽  
Miao Zhang ◽  
Wanqiang Qin ◽  
Jin-Long Wang ◽  
...  
Keyword(s):  
Energy Efficiency ◽  
Optimization Problem ◽  
Type Inequality ◽  
Optimal Solution ◽  
Maximization Problem ◽  
Subtraction Problem ◽  
Channel State ◽  
Convex Optimization Problem ◽  
Single Output ◽  
Optimal Beamforming

In this paper, the optimal beamforming problem of multi-input single-output (MISO) cognitive radio (CR) downlink networks with simultaneous wireless information and power transfer is studied. Due to the nonconvexity of the objective function, the considered nonconvex optimization problem is firstly transformed to an equivalent subtraction problem and then an approximated convex optimization problem is obtained by using the successive convex approximation (SCA). When the instantaneous channel state information (CSI) of the eavesdropping link is unknown to the legitimate transmitter, another interruption-constrained energy efficiency optimization problem is proposed and the Bernstein-type inequality (BTI) is used to conservatively approximate the probability constraint. The paper proposes a two-level iterative algorithm based on Dinkelbach to find the optimal solution of the EE maximization problem. Numerical results validate the effectiveness and convergence of the proposed algorithm.

A Variational Binary Level Set Method for Structural Topology Optimization

2013 ◽  
Vol 13 (5) ◽  
pp. 1292-1308 ◽  
Author(s):  
Xiaoxia Dai ◽  
Peipei Tang ◽  
Xiaoliang Cheng ◽  
Minghui Wu
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Fast Algorithm ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Structural Topology ◽  
Piecewise Constant ◽  
Topology Optimization Problem ◽  
And Topology

AbstractThis paper proposes a variational binary level set method for shape and topology optimization of structural. First, a topology optimization problem is pre-sented based on the level set method and an algorithm based on binary level set method is proposed to solve such problem. Considering the difficulties of coordination between the various parameters and efficient implementation of the proposed method, we present a fast algorithm by reducing several parameters to only one parameter, which would substantially reduce the complexity of computation and make it easily and quickly to get the optimal solution. The algorithm we constructed does not need to re-initialize and can produce many new holes automatically. Furthermore, the fast algorithm allows us to avoid the update of Lagrange multiplier and easily deal with constraints, such as piecewise constant, volume and length of the interfaces. Finally, we show several optimum design examples to confirm the validity and efficiency of our method.

scholarly journals Real-Time Implementation of Green Light Optimal Speed Advisory for Electric Vehicles

Vehicles ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 35-54 ◽  
Author(s):  
Lior Simchon ◽  
Raul Rabinovici
Keyword(s):  
Energy Consumption ◽  
Real Time ◽  
Intelligent Transportation Systems ◽  
Optimization Problem ◽  
Green Light ◽  
Optimal Solution ◽  
Transportation Systems ◽  
Traffic Light ◽  
Calculation Time ◽  
Optimal Speed

Intelligent Transportation Systems (ITS), such as Green Light Optimal Speed Advisory (GLOSA) systems, can be used to reduce the energy consumption in modern vehicles. In particular, GLOSA systems provide driving strategies that can decrease both energy consumption and travel time. In this paper, we present a new method to calculate the optimal driving speeds based on traffic light data. To this end, a detailed formulation for the optimization problem is presented for a multi-segment route, based on an electric vehicle (EV) and traffic light models in an urban environment. Since this formulation results in a nonconvex optimization problem, a relaxation procedure is applied with a low calculation time. By using this procedure, a dynamic real-time speed advisory algorithm is developed. Numerical simulations showed improved performance over benchmark techniques. In particular, the proposed Dynamic-GLOSA solution’s performance was shown to be very close to that with a brute-force optimal solution but with a much shorter calculation time and has significant potential for energy saving.

Sign in / Sign up

Export Citation Format

Share Document