Difference Of Convex Research Articles

Entry trajectory optimization of lifting-body vehicle by successive difference-of-convex programming

The complexity of the three-dimensional entry trajectory optimization problem has escalated due to the need to liberalize the angle of attack and bank angle as control variables, thereby enhancing the inherent maneuverability and control capabilities of lifting-body vehicles. The difference-of-convex (DC) properties inherent in the constraints of the problem are exploited in this paper. A DC decomposition approach is utilized to address the nonlinear auxiliary control equations, and the DC relaxation technique is applied to resolve iteration infeasibilities arising from Taylor expansion. The dependence on the initial trajectory is diminished by the implementation of an exact penalty method, thus improving the applicability of the methods. Furthermore, a control variable oscillation suppression mechanism has been constructed to tackle the control variable oscillation issues arising from the relaxation of the angle of attack and bank angle. This mechanism effectively suppresses large jumps in the angle of attack and high-frequency oscillations in the bank angle. Two novel successive DC programming methods are proposed: the successive concave-convex procedure and the successive proximal bundle method, functioning independently of trust-region constraints. Numerical experiments have demonstrated that the two proposed successive DC optimization methods exhibit exceptional performance in accuracy, feasibility, adaptability, and low sensitivity to initial values when applied to solving the three-dimensional entry trajectory optimization problem.

Probability rate optimization of positive Markov jump linear systems via DC programming

AbstractWe investigate the stabilization problem of positive Markov jump linear systems by optimizing their transition probability rates. By using the convex property of posynomials and the standard mathematical programming that deals with the difference in convex functions, we show that transition probability rate synthesis problems can be solved via difference‐of‐convex (DC) programming. A numerical example is used to illustrate the effectiveness of our results.

An inexact proximal linearized DC algorithm with provably terminating inner loop

Standard approaches to difference-of-convex (DC) programs require exact solution to a convex subproblem at each iteration, which generally requires noiseless computation and infinite iterations of an inner iterative algorithm. To tackle these difficulties, inexact DC algorithms have been proposed, mostly by relaxing the convex subproblem to an approximate monotone inclusion problem. However, there is no guarantee that such relaxation can lead to a finitely terminating inner loop. In this paper, we point out the termination issue of existing inexact DC algorithms by presenting concrete counterexamples. Exploiting the notion of ϵ-subdifferential, we propose a novel inexact proximal linearized DC algorithm termed tPLDCA. Despite permission to a great extent of inexactness in computation, tPLDCA enjoys the same convergence guarantees as exact DC algorithms. Most noticeably, the inner loop of tPLDCA is guaranteed to terminate in finite iterations as long as the inner iterative algorithm converges to a solution of the proximal point subproblem, which makes an essential difference from prior arts. In addition, by assuming the first convex component of the DC function to be pointwise maximum of finitely many convex smooth functions, we propose a computational friendly surrogate of ϵ-subdifferential, whereby we develop a feasible implementation of tPLDCA. Numerical results demonstrate the effectiveness of the proposed implementation of tPLDCA.

Noise and distortion suppression for industrial confocal microscopy

Industrial confocal microscopy is an optical imaging measurement technology used in the fields of material research, defect detection and industrial inspection. Noise will affect the quality of the image and thus affect its performance. We propose a denoising algorithm based on CNN minimisation in this paper. First, we give the object function of the algorithm and the adaptive calculation formula of the capped value. Then, by using the difference convex (DC) optimisation algorithm framework, the sub-gradient optimisation condition, and the feedback framework, we develop a simple and efficient adaptive-stop iterative optimisation algorithm to solve this model and provide the closed solution of the model at each iteration. The experimental results show that for industrial confocal images, our algorithm can not only effectively suppress noise, but also effectively avoid the distortion of denoised images. The signal-to-noise ratio of industrial confocal denoised images is increased by 1.93 times. In addition, experiments show that the algorithm has good noise reduction ability in other optical imaging instruments, and can suppress not only Gaussian noise, but also Gaussian-Poisson noise.

The Descent–Ascent Algorithm for DC Programming

We introduce a bundle method for the unconstrained minimization of nonsmooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent–ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent–ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms – Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0142 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0142 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

An Accelerated Double-Proximal Gradient Algorithm for DC Programming

The double-proximal gradient algorithm (DPGA) is a new variant of the classical difference-of-convex algorithm (DCA) for solving difference-of-convex (DC) optimization problems. In this paper, we propose an accelerated version of the double-proximal gradient algorithm for DC programming, in which the objective function consists of three convex modules (only one module is smooth). We establish convergence of the sequence generated by our algorithm if the objective function satisfies the Kurdyka–[Formula: see text]ojasiewicz (K[Formula: see text]) property and show that its convergence rate is not weaker than DPGA. Compared with DPGA, the numerical experiments on an image processing model show that the number of iterations of ADPGA is reduced by 43.57% and the running time is reduced by 43.47% on average.

Joint Trajectory Design and Power Allocation for UAV Assisted Network With User Mobility

This paper investigates the unmanned aerial vehicle (UAV) assisted wireless communications where the UAV acts as the aerial base station to provide downlink data service to the ground users. We consider a typical hot-spot scenario in which the ground users move towards the target points of interests (PoIs) in groups. The UAV can also fly in air to cope with the movement of users. To maximize the system throughput, an optimization problem is formulated to jointly determine the subchannel assignment, the trajectory of UAV and its power allocation per time slot, where the navigation power of UAV, the co-channel interference as well as the quality of service (QoS) requirements of users are taken into account. As the problem is non-convex and hard to solve, we propose a cascade approach. First, we design a user clustering and pairing algorithm to accomplish the subchannel assignment. Then, we apply the block coordinate descent (BCD) based framework to decompose the remaining problem into the power allocation sub-problem and the trajectory design one. The sub-optimal solution can be gradually achieved through alternatively solving these two sub-problems. As for the power allocation sub-problem, we opt to the difference of convex (DC) functions form and the successive convex approximation (SCA) method to solve it. While for the trajectory design sub-problem, the auxiliary variables and SCA method are utilized. Vivid simulation results reveal that the proposed iterative algorithm can well satisfy the QoS of users and achieve significant performance gain compared with other benchmark schemes.

A bundle-type method for nonsmooth DC programs

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the first serious step. This yields a descent direction for the original objective function, and it is shown that a stepsize of at least one is accepted in this way. Using a line search, even larger stepsizes are possible. The overall method is shown to be globally convergent to critical points of DC programs. The new algorithm is tested and compared to some other solution methods on several examples and realistic applications.

Difference-of-Convex Algorithm with Extrapolation for Nonconvex, Nonsmooth Optimization Problems

In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration technique and the DC algorithm to develop a novel algorithm for the considered problem. We then study the subsequential convergence of our algorithm to a critical point. Furthermore, we justify the global convergence of the whole sequence generated by our algorithm to a critical point and establish its convergence rate under the Kurdyka–Łojasiewicz condition. Numerical experiments on the nonnegative matrix completion problem are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods.

Optimality conditions and DC-Dinkelbach-type algorithm for vector fractional programming problems with ratios of difference of convex functions

In this work, necessary optimality conditions of KKT type for (weak) Pareto optimality are derived and a DC-Dinkelbach-type algorithm is proposed for vector fractional mathematical programs with ratios of difference of convex (DC) functions, and DC constraints, by reducing the latter to a system of scalar parametric problems and using DC tools. The special case of vector fractional programs with ratios of convex functions is also analysed.

Beamforming Design in Short-Packet Transmission for URLLC in Cell-Free Massive MIMO System

Low latency, high reliability, and high data rate are three performance indicators of Ultra-reliable and low latency communication (URLLC) systems, but they are not able to be met simultaneously. Based on the determined latency and reliability requirements, this paper investigates the problem of the weighted sum rate (WSR) in cell-free massive multi-input multi-output (MIMO) system with multiple access points (APs). User-centric access point selection is considered to further reduce the computational complexity for AP used with acceptable performance loss. The transmitting beamforming is designed to mitigate inter-user interference so as to maximize the WSR under the backhaul and transmitting power constraints. Since the proposed problem is non-convex, two algorithms are proposed to solve the problem under the general SINR regime and the high SINR regime, respectively. For the former, we first approximate the objective function with the difference of convex (DC) programming and reformulate the problem into a semi-definite relaxation (SDR) form. Afterward, auxiliary variables are introduced in accordance with the successive convex approximation (SCA) method to further transform the nonconvex problem into a convex one. In the end, the sub-optimal WSR is obtained by iteratively solving a final convex problem. For the latter, the well-known WMMSE method is applied to address the WSR problem. Numerical results demonstrate the efficiency of our proposed algorithm, e.g., the maximum performance gain of the proposed algorithm is about 25% compared to the classical MMSE method. And the user-centric approach achieves 8 times computational complexity reduction with 4% performance loss.

Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems

The Bundle Enrichment Method (BEM-DC) is introduced for solving nonsmooth difference of convex (DC) programming problems. The novelty of the method consists of the dynamic management of the bundle. More specifically, a DC model, being the difference of two convex piecewise affine functions, is formulated. The (global) minimization of the model is tackled by solving a set of convex problems whose cardinality depends on the number of linearizations adopted to approximate the second DC component function. The new bundle management policy distributes the information coming from previous iterations to separately model the DC components of the objective function. Such a distribution is driven by the sign of linearization errors. If the displacement suggested by the model minimization provides no sufficient decrease of the objective function, then the temporary enrichment of the cutting plane approximation of just the first DC component function takes place until either the termination of the algorithm is certified or a sufficient decrease is achieved. The convergence of the BEM-DC method is studied, and computational results on a set of academic test problems with nonsmooth DC objective functions are provided.

Abort orbit determination of launch vehicles based on difference of convex programming

Existing exoatmospheric guidance laws become ineffective when a thrust loss fault (like one or more engines unexpectedly shut down) occurs in a launch vehicle, which makes the nominal orbit unreachable. This paper presents a new abort orbit determination process to determine an abort orbit which the launch vehicle is able to reach. It involves solving at most two optimization problems and the abort orbit may be circular or elliptical. We will present how to transform the nonconvex optimization problems into difference of convex (DC) programming problems which can be solved by existing methods with guaranteed convergence. The main contribution of this paper lies in proposing a relaxation technique to convexify a nonconvex control constraint and the combination of the introduction of new constraints and a relaxation technique to deal with the strict terminal constraints. Validity of the relaxation technique is ensured by theoretical analysis. A unique feature of the transformation process is that the feasible sets defined by both the control constraint and the strict terminal constraints are all enlarged. This brings a critical benefit that the resulting DC programming problems can be very efficiently solved. Thus, an abort orbit determination algorithm, which is based on DC programming, can be designed to very reliably and efficiently determine an abort orbit, which will be demonstrated by numerical examples.

Joint Unmanned Aerial Vehicle Location and Beamforming and Caching Optimization for Cache-Enabled Multi-Unmanned-Aerial-Vehicle Networks

Due to the advantages such as high flexibility, low cost and easy implementation offered by unmanned aerial vehicles (UAVs), a UAV-assisted network is regard as an appealing solution to a seamless coverage, high disaster-tolerant and on-demand wireless system. In this paper, we focus on the downlink transmission in a cache-enabled UAV-assisted wireless communication network, where UAVs cache popular content from a macro base station in advance and cooperatively transfer the content to users. We aim to minimize the average transmission latency of the system and to formulate an optimization problem that jointly optimizes the UAV location, beamforming and caching strategy. However, the formulated problem is very challenging because of its non-convexity and the highly coupled optimization variables. To solve this resulting problem efficiently, we decompose it into two subproblems, namely UAV location and beamforming optimization, and UAV caching strategy optimization. The first subproblem is an NP-hard joint optimization problem, while the second one is a linear programing problem. By adopting the first-order Taylor expansion, we propose a convex optimization algorithm based on the difference-of-convex (DC) method. Specifically, we bring out a method to apply linear approximation in the DC-based algorithm, which is particularly suitable to the problems involving complicated summations. The numerical results demonstrate that the proposed DC-based iterative optimization algorithm can efficiently reduce the average transmission latency of the system.

An optimization framework for RIS-based energy-efficient multi-cell NOMA systems

Non-orthogonal multiple access (NOMA) is a highly promising multiple access strategy for wideband communication systems due to its high spectral efficiency. However, in multi-cell multi-band systems, interference issues can arise from resource sharing among multiple users, which limits the potential of NOMA. To tackle these issues, in this paper, we study a NOMA system where reconfigurable intelligent surfaces (RIS) are employed across multiple cells with multiple users clusters. Specifically, we propose an optimization framework to maximize the system energy efficiency (EE) through jointly designing the transmission beamformer at each base station, the RIS phase shifts and the corresponding binary selection matrix indicating which elements of the RIS should be used to serve a specific cell. Our optimization framework takes into account the minimum rate requirements of users, the successive interference cancellation (SIC) decoding-based rate constraint, fairness among users as well as the maximum allowed transmission power. The resulting non-convex problem is solved by using an alternating optimization algorithm, wherein semidefinite programming (SDP), successive convex approximation (SCA), and penalty-based difference-of-convex (DC) programming are used to reach a solution. Simulation results show that the proposed system outperforms conventional orthogonal access in terms of EE performance, the achievable rate, and power consumption. Also, the results revealed the critical transmission power level for NOMA beyond which the EE starts decaying. Moreover, the proposed NOMA system shows a limited EE performance compared to the conventional orthogonal access as the number of clusters exceeds a certain limit.

Energy-Efficient Optimization in Distributed Massive MIMO Systems for Slicing eMBB and URLLC Services

The fifth generation (5G) communication system aims to support diverse services such as enhanced mobile broadband (eMBB) and ultra-reliable and low-latency communication (URLLC). In order to enable the coexistence of eMBB and URLLC services on a common physical infrastructure, network slicing incorporated in the distributed massive multiple-input multiple-output (DM-MIMO) system is regarded as a promising solution. In this paper, a non-orthogonal slicing scheme is proposed to improve the spectral efficiency, and the short packet transmission is adopted for URLLC to meet the low latency requirement. Through a joint optimization of beamforming and remote radio unit (RRU) selection, we investigate the energy efficiency (EE) maximization problem for the downlink DM-MIMO system. The formulated problem is a mixed integer nonlinear program (MINLP) that we solve by applying some efficient approaches, such as the Dinkelbach method, the reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> -norm and difference of convex (DC) programming. By combining these approaches in one iteration, a double-loop procedure based on semi-definite relaxation (SDR) and successive convex approximation (SCA) is employed to find the suboptimal solution of the problem. Simulation results show that the proposed scheme significantly improves the EE of the DM-MIMO system and efficiently manages resource allocation.

A deep reinforcement learning for energy efficient resource allocation Intelligent Reflecting Surface (IRS) driven Non-Orthogonal Multiple Access Beamforming (NOMA-BF)

This paper proposes a deep reinforcement learning centralized intelligent reflective surface (IRS) assisted non-orthogonal multiple access beamforming (NOMA-BF) system to improve the capacity gains and energy efficiency of next generation wireless communication networks. A single IRS is deployed at base station (BS) and consists of with R reflecting elements which is used to communicate with N single receiver antennas, referred to as centralized deployment of IRS- assisted NOMA. In the proposed central control scheme, we consider the practical situation where the instantaneous Channel State Information (CSI) of the channel between the IRS and the users is unknown. However, its long-term average is known and therefore makes the system more practical. Consequently, we exploit deep reinforcement technique learning technique to investigate the phase shift design and to tackle optimization problem. The energy efficiency problem is formulated as a non-convex optimization problem and is solved using deep and reinforcement learning algorithms. The first order Taylor approximation and difference of convex (DC) programming method using MATLAB tool box has been adopted to obtain the optimal values for power allocation coefficients. For interference mitigation, efficient user clustering along with beamforming algorithm is exploited. The NOMA user interference is tackled efficiently through the proposed algorithms that compute power allocation coefficients along with desirable phase shifts. The closed form expressions for achievable rates and SINR are derived under the required constraints. Simulation results demonstrate that proposed deep learning and reinforcement learning algorithms achieve improved performances in terms of sum rate, energy efficiency and coverage with lower computational complexity and symbol error rate. The computational complexity reduction has been proved both analytically and graphically and is in agreement.

Energy-Efficient Beamforming and Resource Optimization for AmBSC-Assisted Cooperative NOMA IoT Networks

In this manuscript, we present an energy-efficient alternating optimization framework based on the multi-antenna ambient backscatter communication (AmBSC) assisted cooperative non-orthogonal multiple access (NOMA) for next-generation (NG) internet-of-things (IoT) enabled communication networks. Specifically, the energy-efficiency maximization is achieved for the considered AmBSC-enabled multi-cluster cooperative IoT NOMA system by optimizing the active-beamforming vector and power-allocation coefficients (PAC) of IoT NOMA users at the transmitter, as well as passive-beamforming vector at the multi-antenna assisted backscatter node. Usually, increasing the number of IoT NOMA users in each cluster results in inter-cluster interference (ICI) (among different clusters) and intra-cluster interference (among IoT NOMA users). To combat the impact of ICI, we exploit a zero-forcing (ZF) based active-beamforming, as well as an efficient clustering technique at the source node. Further, the effect of intra-cluster interference is mitigated by exploiting an efficient power-allocation policy that determines the PAC of IoT NOMA users under the quality-of-service (QoS), cooperation, SIC decoding, and power-budget constraints. Moreover, the considered non-convex passive-beamforming problem is transformed into a standard semi-definite programming (SDP) problem by exploiting the successive-convex approximation (SCA) approximation, as well as the difference of convex (DC) programming, where Rank-1 solution of passive-beamforming is obtained based on the penalty-based method. Furthermore, the numerical analysis of simulation results demonstrates that the proposed energy-efficiency maximization algorithm exhibits an efficient performance by achieving convergence within only a few iterations.

New mixed integer fractional programming problem and some multi-objective models for sparse optimization

We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of the problem, which comes out in the form of a fractional programming problem (FPP). In particular, we consider a possible way for tackling FPP by reformulating it via a DC (Difference of Convex) decomposition. We also overview the SVM models and the related Feature Selection in terms of multi-objective optimization. The results of some numerical experiments on benchmark classification datasets are reported.

Transmissive Reconfigurable Intelligent Surface Transmitter Empowered Cognitive RSMA Networks

In this paper, we investigated the downlink transmission problem of a cognitive radio network (CRN) equipped with a novel transmissive reconfigurable intelligent surface (TRIS) transmitter. In order to achieve low power consumption and high-rate multi-streams communication, time-modulated arrays (TMA) is implemented and users access the network using rate splitting multiple access (RSMA). With such a network framework, a multi-objective optimization problem with joint design of the precoding matrix and the common stream rate is constructed to achieve higher energy efficiency (EE) and spectral efficiency (SE). Since the objective function is a non-convex fractional function, we proposed a joint optimization algorithm based on difference-of-convex (DC) programming and successive convex approximation (SCA). Numerical results show that under this framework the proposed algorithm can considerably improve and balance the EE and SE.