Slow Adaptive OFDMA Systems Through Chance Constrained Programming

Adaptive OFDMA has recently been recognized as a promising technique for providing high spectral efficiency in future broadband wireless systems. The research over the last decade on adaptive OFDMA systems has focused on adapting the allocation of radio resources, such as subcarriers and power, to the instantaneous channel conditions of all users. However, such "fast" adaptation requires high computational complexity and excessive signaling overhead. This hinders the deployment of adaptive OFDMA systems worldwide. This paper proposes a slow adaptive OFDMA scheme, in which the subcarrier allocation is updated on a much slower timescale than that of the fluctuation of instantaneous channel conditions. Meanwhile, the data rate requirements of individual users are accommodated on the fast timescale with high probability, thereby meeting the requirements except occasional outage. Such an objective has a natural chance constrained programming formulation, which is known to be intractable. To circumvent this difficulty, we formulate safe tractable constraints for the problem based on recent advances in chance constrained programming. We then develop a polynomial-time algorithm for computing an optimal solution to the reformulated problem. Our results show that the proposed slow adaptation scheme drastically reduces both computational cost and control signaling overhead when compared with the conventional fast adaptive OFDMA. Our work can be viewed as an initial attempt to apply the chance constrained programming methodology to wireless system designs. Given that most wireless systems can tolerate an occasional dip in the quality of service, we hope that the proposed methodology will find further applications in wireless communications

A distributionally robust perspective on uncertainty quantification and chance constrained programming

The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones

Unit Commitment with Load Uncertainty by Joint Chance-Constrained Programming

This paper presents an algorithm to solve a unit commitment problem that takes into account the uncertainty in the demand. This uncertainty is included in the optimization problem as a joint chance constraint that bounds the minimum value of the probability to jointly meet the deterministic power balance constraints. The demand is modeled as a multivariate, normally distributed, random variable and the correlation among different time periods is also considered. A deterministic mixed-integer linear programming problem is sequentially solved until it converges to the solution of the chanceconstrained optimization problem. Different approaches are presented to update the z-value used to transform the joint chance constraint into a set of deterministic constraints. Results from a realistic size case study are presented and the values obtained for the multivariate normal distribution probability are compared with the ones obtained by using a Monte Carlo simulation procedureUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Distribution-free, uniformly-tighter linear approximations for chance-constrained programming

Includes bibliographical references (p. 21-23).Research partially supported by the Leaders for Manufacturing Program.Gabriel R. Bitran, Thin-Yin Leong

A Capital Budgeting Model under Risk with Chance-Constrained Programming

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Safety first portfolio choice based on financial and sustainability returns

This paper lays the mathematical foundations of the notion of an investment's sustainability return and investigates three different models of portfolio selection with probabilistic constraints for safety first investors caring about the financial and the sustainability consequences of their investments. The discussion of these chance-constrained programming problems for stochastic and deterministic sustainability returns includes theoretical results especially on the existence of a unique solution under certain conditions, an illustrating example, and a computational time analysis. Furthermore, we conclude that a simple convex combination of financial and sustainability returns - yielding a new univariate decision variable - is not sufficiently general.Finance; Socially Responsible Investing; Sustainability Value; Safety First Investor