Signomial Programming Problem Research Articles

Joint Hovering Height, Power, and Rate Optimization for Air-to-Ground UAV-RSMA Covert Communications

In this paper, we investigate covert communications for an unmanned aerial vehicle (UAV)-aided rate-splitting multiple access (RSMA) system in which the UAV transmits to the covert and public users separately while shielding covert transmissions from a warden. Under the RSMA principles, the messages of the covert and public users are converted to common and private streams for air-to-ground transmissions. Subject to the quality of service (QoS) requirements of the public user and covertness constraint of the UAV-aid RSMA (UAV-RSMA) system, the aim of covert communication design is to maximize the covert rate by jointly optimizing the transmit power allocation, common rate allocation, and UAV hovering height, which each contribute to the uncertainty of the warden’s binary decision and attempts to enhance communication performance. To address the non-convex covert rate maximization problem in addition to the highly coupled system parameters, we decouple the original problem into three subproblems of transmit power allocation, common rate allocation, and UAV hovering height. We derive the optimal solutions for each of the subproblems of the transmit power and rate allocations and formulate a signomial programming problem to tackle UAV hovering height optimization. The simulation results indicate the superior covert rate performance achieved by the proposed AO algorithm and demonstrate that the proposed UAV-RSMA scheme achieves a higher covert rate than the benchmark schemes.

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

Fuzzy fractional signomial programming problem is a relatively new optimization problem. In real world problems, some variables may vacillate because of various reasons. To tackle these vacillating variables, vagueness is considered in form of fuzzy sets. In this paper, a nonlinear fuzzy fractional signomial programming problem is considered with all its coefficients in objective functions as well as constraints are fuzzy numbers. Two solution approaches are developed based on signomial geometric programming comprising nearest interval approximation with parametric interval valued functions and fuzzy α-cut with min–max approach. To demonstrate the proposed methods, two illustrative numerical examples are solved and the results are comparatively discussed showing its feasibility and effectiveness.

Sparse FIR Filter Design Based on Signomial Programming

The goal of sparse FIR filter design is to minimize the number of nonzero filter coefficients, while keeping its frequency response within specified boundaries. Such a design can be formally expressed via minimization of l0-norm of filter’s impulse response. Unfortunately, the corresponding minimization problem has combinatorial complexity. Therefore, many design methods are developed, which solve the problem approximately, or which solve the approximate problem exactly. In this paper, we propose an approach, which is based on the approximation of the l0-norm by an lp-norm with 0 < p < 1. We minimize the lp-norm using recently developed method for signomial programming (SGP). Our design starts with forming a SGP problem that describes filter specifications. The optimum solution of the problem is then found by using iterative procedure, which solves a geometric program in each iteration. The filters whose magnitude responses are constrained in minimax sense are considered. The design examples are provided illustrating that the proposed method, in most cases, results in filters with higher sparsity than those of the filters obtained by recently published methods.

Joint Time and Power Allocation in Multi-Cell Wireless Powered Communication Networks

This paper investigates the joint time and power allocation in a multi-cell wireless powered communication network (WPCN) with successive interference cancellation. In the WPCN, the hybrid access points broadcast wireless energy to all users and then the users utilize the harvested energy to transmit information simultaneously in a spectrum-sharing fashion. The max-min fairness throughput optimization and max-sum throughput optimization problems are formulated to analyze the system performance. However, both of the two optimization problems are nonconvex due to the complicated co-channel interference and the coupled time and power variables. To deal with this challenge, efficient two-stage approaches are proposed to transform them into more tractable ones. Specifically, for the max-min fairness throughput optimization problem, we first convert the power allocation problem into geometric programming (GP) problem for given time allocation and then optimize the time allocation. For the max-sum throughput optimization problem, we first transform the power allocation problem into a signomial programming problem with fixed time allocation, which is further approximated as a GP one. Then, time allocation is optimized. The simulation results validate the effectiveness of the two proposed approaches. In addition, it is shown that the “doubly near-far” issue can be well addressed by the max-min fairness throughput optimization.

An enhanced logarithmic method for signomial programming with discrete variables

Signomial programming problems with discrete variables (SPD) appear widely in real-life applications, but they are hard to solve. This paper proposes an enhanced logarithmic method to reformulate the SPD problem as a mixed 0-1 linear program (MILP) with a minimum number of binary variables and inequality constraints. Both of the theoretical analysis and numerical results strongly support its superior performance to other state-of-the-art linearization methods. We also extend the proposed method to linearize some more complicated problems involving product and fractional terms in discrete and continuous variables.

Global optimisation of a portfolio adjustment problem under credibility measures

In this paper it is shown how to find the guaranteed e-optimal solution to the credibilistic portfolio adjustment problem in the formulation presented by Zhang et al. (2010). In its crisp form, the problem is a non-convex signomial programming problem. This type of problem is difficult to solve to global optimality and solving it using a non-global solver may give suboptimal solutions. Using the signomial global optimisation (SGO) algorithm, it is however possible to reformulate the problem into a convex problem whose feasible region overestimates that of the non-convex problem in an extended variable space. The overestimation is iteratively reduced until the global solution is found. To illustrate the procedure, the SGO algorithm is applied to the example in the original article. It is shown that the solutions presented were only local ones, and the global solution corresponding to better portfolio adjustment strategies is given.

Multi-Rate Resource Allocations for TH-UWB Wireless Communications

In this paper, we are interested in resource allocation strategies for wireless time-hopping ultra-wide band (TH-UWB) communications with multiple rate capabilities between users. Multiple rates are achieved by assigning different processing gains, i.e. N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> , to users. For this purpose, the multiple-access interference (MAI) variance accounting for multi-rate is needed. It is a challenging task due to the lack of a suitable closed-form expression for the MAI variance in a multi-rate context. We further study the multi-rate resource allocation problem in uplink TH-UWB systems for which an optimal search cannot be envisaged due to the exponential complexity induced. Our contribution lies in three-fold: i) A new intercode correlation expression accounting for multi-rate communications is derived, and the variance of the MAI averaging over the codes is obtained. ii) The multi-rate resource allocation problem is tackled by relaxing the integer constraint on the processing gains and modeled via a signomial programming problem. iii) Based on this, a branch and bound (BB) algorithm is derived for the allocation of the processing gains in TH-UWB systems. We also propose a really simple heuristic with linear complexity for the N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> allocation. We show that the algorithm proposed outperforms the BB algorithm in average throughput and average starvation rate.

A Review of Deterministic Optimization Methods in Engineering and Management

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed‐integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

Designing globally optimal delta–sigma modulator topologies via signomial programming

AbstractWe present a design methodology for globally optimizing the topologies of delta–sigma modulators (DSMs). Previous work cast the design task into a general non‐convex, nonlinear programming problem, whereas we propose to recast it as a signomial programming problem. Convexification strategies are presented for transforming the signomial programming problem into its equivalent convex counterpart, thereby enabling the solution of globally optimal design parameters. It is also possible to include circuit non‐ideal effects that affect the transfer function of the modulator into the formulation without affecting the computational efficiency. The proposed framework has been applied to topology synthesis problems of single‐loop and multi‐loop low‐pass DSMs based on discrete‐time circuitry. Numerical results confirm the effectiveness of the proposed approach over conventional nonlinear programming techniques. Copyright © 2008 John Wiley &amp; Sons, Ltd.

On the mixed integer signomial programming problems

This paper proposes an approximate method to solve the mixed integer signomial programming problem, for which the objective function and the constraints may contain product terms with exponents and decision variables, which could be continuous or integral. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a signomial term into the sum of absolute terms; these absolute terms are then linearized by linearization strategies. In addition, a novel approach is included for solving integer and undefined problems in the logarithmic piecewise technique, which leads to more usefulness of the proposed method. The proposed method could reach a solution as close as possible to the global optimum.

Optimal design of a membrane separation process using signomial programming

A multistage membrane separation process for hydrogen recovery is described and formulated as a signomial programming problem. Two different configurations are examined. A 3-stage and a 5-stage process design problem are solved. The optimal solution to these programs is computed from an initial point that does not satisfy the mass balance or transport constraints of the process, using a primal-based geometric programming code. Also examined is the sensitivity of the optimal solution to changes in purity requirements. In all cases, computation times are very reasonable ranging from 2 to 4 seconds of IBM 370/165 CPU time.

COMPUTATIONAL ASPECTS OF GEOMETRIC PROGRAMMING 3. SOME PRIMAL AND DUAL ALGORITHMS FOR POSYNOMIAL AND SIGNOMIAL GEOMETRIC PROGRAMS

In this paper we consider algorithmic and computational aspects of selected methods for posynomial and signomial programming problems. In particular, we consider the modified concave simplex method for dual posynomial programs and discuss some recent developments suggesting a new dual algorithm. We also consider linear programming based algorithms for primal posynomial programs. Finally, we discuss a recently developed branch and bound method for signomial programming.