Nonlinear Fractional Programming

By I. Stancu-Minasian. 1997

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Citations in the corpus

Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “In his seminal work Dinkelbach (1967) and later Zhang (2008) proposed a novel framework to solve constrained QFP problems by converting it to an equivalent parametric optimization problem, by introducing a scalar parameter α ∈ R.”
All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, methodology): “We achieve this by minimizing a series of linear objective functions in the form of ĥ−,γ , using a similar method to that of Dinkelbach (1967). Often, minimizing the linear combination ĥ−,γ(f) is more tractable than minimizing the MR ratio directly.”
Energy-Efficient UAV-Assisted Mobile Edge Computing: Resource Allocation and Trajectory Optimization (2020, unknown): “Due to the monotone decreasing property of F t ( α ) , F t ( α ∗ ) = 0 if and only if α ∗ is equal to the optimal result of problem (20), i.e. , α ∗ = ˇ η ( ∗ ; A t ) [33].”
Secrecy Rate Maximization for Intelligent Reflecting Surface Assisted Multi-Antenna Communications (2019, methodology): “Then, the optimal objective value of problem (7) is the unique root of ψ(μ) = 0 [17].”
On Cooperative Relaying Schemes for Wireless Physical Layer Security (2010, methodology): “The relation between and the problem of (32) is given in the following property [27].”
Framework for Link-Level Energy Efficiency Optimization with Informed Transmitter (2011, unknown): “At the optimum, the inequality in the dual problem is satisfied with equality, i.e. −f1(x∗) + λ∗f2(x∗) + (g(x∗))Tu∗ = 0.”
All Models are Wrong but many are Useful: Variable Importance for Black-Box, Proprietary, or Misspecified Prediction Models, using Model Class Reliance (2018, methodology): “ < 2e^ orig(f) + ^e switch(f) ^h ; 1(f) <^h ; 2(f): (C.6) Applying this, we have ^h ; 1(^g ; 1) ^h ; 1(^g ; 2) from Eq C.2 ^h ; 2(^g ; 2) from Eq C.6: This result is analogous to Lemma 3 from Dinkelbach (1967). C.2.2 Part 2: e^ orig(^g ; ) is Monotonically Decreasing in . Let 1; 2 2R satisfy 1”
Wireless Information and Power Transfer: Energy Efficiency Optimization in OFDMA Systems (2013, methodology): “Iterative Algorithm for Energy Efficiency Maximization In this section, an iterative algorithm (known as the Dinkelbach method7 [22]) is proposed for solving (8) with an equivalent objective function such that the obtained solution satisfies the conditions stated in Theorem 1.”
Optimal Joint Power and Subcarrier Allocation for Full-Duplex Multicarrier Non-Orthogonal Multiple Access Systems (2016, background): “The problem in (23) is a standard fractional programming problem which can be solved by the Dinkelbach algorithm [29] in polynomial time.”
Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching (2018, methodology): “Part I of this paper [3] proposes a novel quadratic transform technique to tackle FP problems involving multiple ratios, which are frequently encountered in communication system design, but are typically beyond the capabilities of classic FP techniques, such as Schaible’s transform [4] and Dinkelbac”
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling (2010, unknown): “…= Ng ∑ g=1 γgrΦg(fk)+σ 2 r+er(fk) = [ Ng ∑ g=1 Nb ∑ ν=1 γgrbν(fk)]xgν+σ 2 r+er(fk) = a T r (fk)xo+er(fk) (37) where the PSDΦg(f) is nonzero only if a transmitting source is present atlg; γgr represents the channel gain from the candidate source atlg to the CR atℓr that is assumed to…”
A Convolutional Learning System for Object Classification in 3-D Lidar Data (2010, methodology): “The subsampling layer uses trainable weights, i.e., the multiplier weight (1/8 in the example above) and the bias weight.”
Secure Radar-Communication Systems With Malicious Targets: Integrating Radar, Communications and Jamming Functionalities (2019, methodology): “Following [34], (15) is single-ratio FP problem, which can be solved by employing the Dinkelbach’s transform demonstrated in [44], where the globally optimal solution can be obtained by solving a sequence of SDPs.”
Computation Offloading and Resource Allocation in Mixed Fog/Cloud Computing Systems With Min-Max Fairness Guarantee (2018, methodology): “To tackle the difficulty, we replace V ∗ with an update parameter V [29].”
IRS-Assisted Secure UAV Transmission via Joint Trajectory and Beamforming Design (2022, background): “…solving First, introduce an auxiliary vector u Based on this, the problem (18) can be rewritten as where To make it solvable, we further transform (19) into an equivalent form as which belongs to fractional programming and can be converted into a series of parametric sub-problems according to [36].”
Energy Efficient Federated Learning Over Wireless Communication Networks (2019, methodology): “Thus, problem (23) can be solved by using the Dinkelbach method in [38] (shown as Algorithm 2).”
Energy Efficient Multi-User MISO Communication Using Low Resolution Large Intelligent Surfaces (2018, methodology): “Hence, problem (14) can be globally solved with limited complexity using Dinkelbach’s method [29], as presented in Algorithm 1.”
Enhanced lasso recovery on graph (2015, unknown): “(3ii) xn+1 = x n−ηnpn+1+EkληnU∗f0+E kηnyk/τk 1+Ekληn+Ekηn/τk (3iii) θn+1 = 1/ √ 1 + 2γηn, τn+1 = θn+1ηn, σn+1 = σn/θn+1 (3iv) x̄n+1 = xn+1 + θn+1(xn+1 − xn) (4) xk = xn+1 Note: the time step τk = Bk was chosen experimentally, and is the subject of future study.”