Variations and extension of the convex–concave procedure

Lipp, Thomas; Boyd, Stephen

doi:10.1007/s11081-015-9294-x

Cited by 676 publications

(596 citation statements)

References 74 publications

Supporting

Mentioning

591

Contrasting

Unclassified

Order By: Relevance

“…Hence, it can be shown that the sequence of objective values generated by Algorithm 1 is nonincreasing [30]. Moreover, the optimal objective value of problem (9) is bounded.…”

Section: F Convergence Of Algorithm 1 and Algorithmmentioning

confidence: 97%

“…However, it is still nonconvex because the objective function is concave and constraint function (9a) is not convex. In the sequel, we apply sequential convex programming [30] to solve problem (9). Here, we approximate the objective function and constraint function (9a) with their best convex approximations.…”

Section: A Centralized Algorithmmentioning

confidence: 99%

“…The best convex approximation of constraint function (9a) near an arbitrary point (m ki ,β ki ) can be obtained by replacing g ki (m ki , β ki ) with its first order approximation [30], and it can be expressed aŝ (11) where…”

Section: A Centralized Algorithmmentioning

confidence: 99%

“…In all our simulations, Algorithm 1 is stopped if the improvement in the objective value is less than some κ [30], where we set κ = 0.01. In Algorithm 2, the ADMM algorithm (i.e., the inner iterations) is stopped after running a fixed number of iterations Q [31,Ch.…”

Section: Max-min Fair Admission Controlmentioning

confidence: 99%

“…In the case of static networks, the centralized algorithm is derived by using sequential convex programming [30]. Unlike the deflation based algorithm in [2] that relies on dropping a user at each iteration until the maximum number of admitted users is found, the proposed algorithm decides the admissibility of users only when it converges.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Admission Control Algorithms for QoS-Constrained Multicell MISO Downlink Systems

Manosha

Joshi

Codreanu

et al. 2018

IEEE Trans. Wireless Commun.

View full text Add to dashboard Cite

Abstract-The problem of admission control in a multicell downlink multiple-input single-output system is considered. The objective is to maximize the number of admitted users subject to the signal-to-interference-plus-noise ratio constraint for each admitted user and a transmit power constraint at each base station. We cast the admission control problem as an 0 minimization problem. This problem is known to be combinatorial NP-hard. Hence, we have to rely on suboptimal algorithms to solve it. We first approximate the 0 minimization problem via a non-combinatorial one. Then, we propose centralized and distributed algorithms to solve the non-combinatorial problem. To develop the centralized algorithm, we use the sequential convex programming method. The distributed algorithm is derived by using the alternating direction method of multipliers in conjunction with sequential convex programming. We show numerically that the proposed admission control algorithms achieve a near-to-optimal performance. Next, we extend the admission control problem to provide fairness, where a long term fairness among the users is guaranteed. We focus on proportional and max-min fairness and propose dynamic control algorithms via Lyapunov optimization. It is shown numerically that the proposed fair admission control algorithms guarantee fairness among the users.

show abstract

“…Hence, it can be shown that the sequence of objective values generated by Algorithm 1 is nonincreasing [30]. Moreover, the optimal objective value of problem (9) is bounded.…”

Section: F Convergence Of Algorithm 1 and Algorithmmentioning

confidence: 97%

Section: A Centralized Algorithmmentioning

confidence: 99%

Section: A Centralized Algorithmmentioning

confidence: 99%

Section: Max-min Fair Admission Controlmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Admission Control Algorithms for QoS-Constrained Multicell MISO Downlink Systems

Manosha

Joshi

Codreanu

et al. 2018

IEEE Trans. Wireless Commun.

View full text Add to dashboard Cite

show abstract

Psse Redux

Kekatos

Wang

Zhu

et al. 2020

Advances in Electric Power and Energy

View full text Add to dashboard Cite

Minimax A‐, c‐, and I‐optimal regression designs for models with heteroscedastic errors

Abousaleh

Zhou

2021

Can J Statistics

View full text Add to dashboard Cite

It is well known that it is difficult to construct minimax optimal designs. Furthermore, since in practice we never know the true error variance, it is important to allow small deviations and construct robust optimal designs. We investigate a class of minimax optimal regression designs for models with heteroscedastic errors that are robust against possible misspecification of the error variance. Commonly used A‐, c‐, and I‐optimality criteria are included in this class of minimax optimal designs. Several theoretical results are obtained, including a necessary condition and a reflection symmetry for these minimax optimal designs. In this article, we focus mainly on linear models and assume that an approximate error variance function is available. However, we also briefly discuss how the methodology works for nonlinear models. We then propose an effective algorithm to solve challenging nonconvex optimization problems to find minimax designs on discrete design spaces. Examples are given to illustrate minimax optimal designs and their properties.

show abstract

Variations and extension of the convex–concave procedure

Cited by 676 publications

References 74 publications

Admission Control Algorithms for QoS-Constrained Multicell MISO Downlink Systems

Admission Control Algorithms for QoS-Constrained Multicell MISO Downlink Systems

Psse Redux

Minimax A‐, c‐, and I‐optimal regression designs for models with heteroscedastic errors

Contact Info

Product

Resources

About