An associated maximization problem for two-person nonzero-sum separable games

1976 ◽  
Vol 10 (1) ◽  
pp. 124-129
Author(s):  
L. C. Westphal
Keyword(s):  
Maximization Problem ◽  
Separable Games

The associated maximization problem for separable games

1973 ◽  
Vol 5 (1) ◽  
pp. 374-380 ◽  
Author(s):  
L. C. Westphal ◽  
A. R. Stubberud
Keyword(s):  
Maximization Problem ◽  
Separable Games

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Genetic Algorithm for the Retailers’ Shelf Space Allocation Profit Maximization Problem

2021 ◽  
Vol 11 (14) ◽  
pp. 6401
Author(s):  
Kateryna Czerniachowska ◽  
Karina Sachpazidu-Wójcicka ◽  
Piotr Sulikowski ◽  
Marcin Hernes ◽  
Artur Rot
Keyword(s):  
Genetic Algorithm ◽  
Profit Maximization ◽  
Allocation Rule ◽  
Maximization Problem ◽  
Shelf Space ◽  
Allocation Model ◽  
Space Allocation ◽  
Shelf Space Allocation ◽  
To Receive

This paper discusses the problem of retailers’ profit maximization regarding displaying products on the planogram shelves, which may have different dimensions in each store but allocate the same product sets. We develop a mathematical model and a genetic algorithm for solving the shelf space allocation problem with the criteria of retailers’ profit maximization. The implemented program executes in a reasonable time. The quality of the genetic algorithm has been evaluated using the CPLEX solver. We determine four groups of constraints for the products that should be allocated on a shelf: shelf constraints, shelf type constraints, product constraints, and virtual segment constraints. The validity of the developed genetic algorithm has been checked on 25 retailing test cases. Computational results prove that the proposed approach allows for obtaining efficient results in short running time, and the developed complex shelf space allocation model, which considers multiple attributes of a shelf, segment, and product, as well as product capping and nesting allocation rule, is of high practical relevance. The proposed approach allows retailers to receive higher store profits with regard to the actual merchandising rules.

scholarly journals Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Yaoxin Li ◽  
Jing Liu ◽  
Guozheng Lin ◽  
Yueyuan Hou ◽  
Muyun Mou ◽  
...  
Keyword(s):  
Objective Function ◽  
Statistical Physics ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Independent Set ◽  
Computational Social Science ◽  
Maximization Problem ◽  
Maximum Independent Set ◽  
Gradient Descent Algorithm

AbstractIn computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

scholarly journals Improving Energy Efficiency Fairness of Wireless Networks: A Deep Learning Approach

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4300 ◽  
Author(s):  
Hoon Lee ◽  
Han Seung Jang ◽  
Bang Chul Jung
Keyword(s):  
Energy Efficiency ◽  
Wireless Networks ◽  
Deep Learning ◽  
Power Control ◽  
Control Method ◽  
Optimal Solution ◽  
Control Policy ◽  
Maximization Problem ◽  
Optimization Approach ◽  
Conventional Optimization

Achieving energy efficiency (EE) fairness among heterogeneous mobile devices will become a crucial issue in future wireless networks. This paper investigates a deep learning (DL) approach for improving EE fairness performance in interference channels (IFCs) where multiple transmitters simultaneously convey data to their corresponding receivers. To improve the EE fairness, we aim to maximize the minimum EE among multiple transmitter–receiver pairs by optimizing the transmit power levels. Due to fractional and max-min formulation, the problem is shown to be non-convex, and, thus, it is difficult to identify the optimal power control policy. Although the EE fairness maximization problem has been recently addressed by the successive convex approximation framework, it requires intensive computations for iterative optimizations and suffers from the sub-optimality incurred by the non-convexity. To tackle these issues, we propose a deep neural network (DNN) where the procedure of optimal solution calculation, which is unknown in general, is accurately approximated by well-designed DNNs. The target of the DNN is to yield an efficient power control solution for the EE fairness maximization problem by accepting the channel state information as an input feature. An unsupervised training algorithm is presented where the DNN learns an effective mapping from the channel to the EE maximizing power control strategy by itself. Numerical results demonstrate that the proposed DNN-based power control method performs better than a conventional optimization approach with much-reduced execution time. This work opens a new possibility of using DL as an alternative optimization tool for the EE maximizing design of the next-generation wireless networks.

Representing Social Construction in Consumer Activities: Single-Period and Multi-Period Activity Production

1994 ◽  
Vol 5 (3) ◽  
pp. 139-156
Author(s):  
Steven D. Silver
Keyword(s):  
Social Construction ◽  
Evolutionary Process ◽  
Decision Makers ◽  
Maximization Problem ◽  
Activity Levels ◽  
Short Term ◽  
Subsequent Period ◽  
Single Period ◽  
The Social ◽  
Endogenous Variables

Consumers are seen as limited decision makers who set short-term activity levels from their budgets, stocks of experience, and values following a preference-maximizing heuristic. Disturbances to activity levels in their evolution by exogeneties of social and economic environments, and the feedback of activity levels which agents have no systematic ability to anticipate, reset stock and value levels through the interactive relationships among endogenous variables. Agents then solve the maximization problem for a subsequent period using stock and value levels as modified by the evolutionary process. The dependence of a single-period decision on the stock and value constructs is examined and forms for the dynamic evolution of stock and value constructs that represent the feedback of activity levels to stock and value levels are also introduced. Implications of these forms for the social construction of activities are discussed.

scholarly journals Entry and Exit Decision Problem with Implementation Delay

2008 ◽  
Vol 45 (04) ◽  
pp. 1039-1059 ◽  
Author(s):  
Marius Costeniuc ◽  
Michaela Schnetzer ◽  
Luca Taschini
Keyword(s):  
Decision Problem ◽  
Analytic Solution ◽  
Time Lag ◽  
Probabilistic Approach ◽  
Stopping Time ◽  
Stopping Times ◽  
Maximization Problem ◽  
Entry And Exit ◽  
Brownian Motion With Drift ◽  
Implementation Delay

We study investment and disinvestment decisions in situations where there is a time lagd> 0 from the timetwhen the decision is taken to the timet+dwhen the decision is implemented. In this paper we apply the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay. In particular, we prove the independence between Parisian stopping times and a general Brownian motion with drift stopped at the stopping time. Relying on this result, we solve the constrained maximization problem, obtaining an analytic solution to the optimal ‘starting’ and ‘stopping’ levels. We compare our results with the instantaneous entry and exit situation, and show that an increase in the uncertainty of the underlying process hastens the decision to invest or disinvest, extending a result of Bar-Ilan and Strange (1996).

scholarly journals A Novel Integrated Profit Maximization Model for Retailers under Varied Penetration Levels of Photovoltaic Systems

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 92
Author(s):  
Ioannis P. Panapakidis ◽  
Nikolaos Koltsaklis ◽  
Georgios C. Christoforidis
Keyword(s):  
Profit Maximization ◽  
Energy Markets ◽  
Maximization Problem ◽  
Selling Price ◽  
Retail Market ◽  
Stochastic Variable ◽  
Wholesale Market ◽  
Market Operation ◽  
Pv Penetration ◽  
Marginal Price

In contemporary energy markets, the Retailer acts as the intermediate between the generation and demand sectors. The scope of the Retailer is to maximize its profits by selecting the appropriate procurement mechanism and selling price to the consumers. The wholesale market operation influences the profits since the mix of generation plants determines the system marginal price (SMP). In the related literature, the SMP is treated as a stochastic variable, and the wholesale market conditions are not taken into account. The present paper presents a novel methodology that aims at connecting the wholesale and retail market operations from a Retailer’s perspective. A wholesale market clearing problem is formulated and solved. The scope is to examine how different photovoltaics (PV) penetration levels in the generation side influences the profits of the Retailer and the selling prices to the consumers. The resulting SMPs are used as inputs in a retailer profit maximization problem. This approach allows the Retailer to minimize economic risks and maximize profits. The results indicate that different PV implementation levels on the generation side highly influences the profits and the selling prices.

scholarly journals Non-submodular model for group profit maximization problem in social networks

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Jianming Zhu ◽  
Smita Ghosh ◽  
Weili Wu ◽  
Chuangen Gao
Keyword(s):  
Social Networks ◽  
Profit Maximization ◽  
Randomized Algorithm ◽  
Political Orientation ◽  
Submodular Functions ◽  
Maximization Problem ◽  
Modular Algorithm ◽  
The Difference ◽  
Group Enterprise ◽  
Theoretical Results

AbstractIn social networks, there exist many kinds of groups in which people may have the same interests, hobbies, or political orientation. Sometimes, group decisions are made by simply majority, which means that most of the users in this group reach an agreement, such as US Presidential Elections. A group is called activated if $$\beta$$ β percent of users are influenced in the group. Enterprise will gain income from all influenced groups. Simultaneously, to propagate influence, enterprise needs pay advertisement diffusion cost. Group profit maximization (GPM) problem aims to pick k seeds to maximize the expected profit that considers the benefit of influenced groups with the diffusion cost. GPM is proved to be NP-hard and the objective function is proved to be neither submodular nor supermodular. An upper bound and a lower bound which are difference of two submodular functions are designed. We propose a submodular–modular algorithm (SMA) to solve the difference of two submodular functions and SMA is shown to converge to a local optimal. We present an randomized algorithm based on weighted group coverage maximization for GPM and apply sandwich framework to get theoretical results. Our experiments verify the efficiency of our methods.

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