MINIMUM DISCRIMINATION INFORMATION PROBLEMS VIA GENERALIZED GEOMETRIC PROGRAMMING

In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties of the generalized geometric programming,the dual programs of these two problems are derived.Furthermore,the duality theorems and related Kuhn-Tucker conditions for two pairs of the prime-dual programs are also established by the duality theory.

An Alternative Approach to the Solution of Multi-Objective Geometric Programming Problems

The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.

Compromising Solution of Geometric Programming Problem with Bounded Parameters

This paper addresses a geometric programming problem,where the objective function and constraints are interval-valued functions.The concept of acceptable feasible region is introduced,and a methodology is developed to transform this model to a general optimization problem,which is free from interval uncertainty.Relationship between the solution of the original problem and the transformed problem is established.The methodology is illustrated through numerical examples.Solutions by the proposed method and previous methods are analyzed.

Optimization Design of Two-Stage Operational Amplifier with Frequency Compensation via Geometric Programming

An optimization design technique to obtain global solution for a two-stage operational amplifier(op-amp) with frequency compensation is presented.This frequency compensation technique can adjust the equivalent resistance to guarantee that the phase margin is stable even though circumstance temperature varies.Geometric programming is used to optimize the component values and transistor dimensions.It is used in this analog integrated circuit design to calculate these parameters automatically.This globally optimal amplifier obtains minimum power while other specifications are fulfilled.

Capacity Analysis and Sum Rate Maximization for the SCMA Cellular Network Coexisting with D2D Communications

Sparse code multiple access (SCMA) is the most concerning scheme among non-orthogonal multiple access (NOMA) technologies for 5G wireless communication new interface. Another efficient technique in 5G aimed to improve spectral efficiency for local communications is device-to-device (D2D) communications. Therefore, we utilize the SCMA cellular network coexisting with D2D communications for the connection demand of the Internet of things (IOT), and improve the system sum rate performance of the hybrid network. We first derive the information-theoretic expression of the capacity for all users and find the capacity bound of cellular users based on the mutual interference between cellular users and D2D users. Then we consider the power optimization problem for the cellular users and D2D users jointly to maximize the system sum rate. To tackle the non-convex optimization problem, we propose a geometric programming (GP) based iterative power allocation algorithm. Simulation results demonstrate that the proposed algorithm converges fast and well improves the sum rate performance.

Optimal quality level,order quantity and selling price for the retailer in a two-level supply chain

For a classical order quantity/pricing problem,we present a geometric programming(GP)approach to find the optimal selling price,order quantity and quality level to maximize the profit for the retail firm.Traditional models such as EOQ are not able to handle the nonlinearity of costs and demand.We adopt the GP approach and make a proper transformation of the model so as to solve this classical problem and obtain the global optimal solution.In addition to the optimal solutions,we also perform a sensitivity analysis.The study shows once more that GP is an excellent approach when decision variables interact in a nonlinear,especially exponential manner.

Quality of service aware admission control in cognitive device-to-device network

A hybrid system of cellular mode and device-to-device （D2D） mode is considered in this paper, where the cellular resource is reused by the D2D transmission. With the objective of capacity maximization, the power optimization of D2D sub-system is considered, taking into account quality of service （QoS） requirement. The power optimization problem is divided into two stages： The first stage is the admission control scheme design based on the QoS requirement of D2D users, and the second is power allocation to maximize aggregate throughput of admissible D2D users. For the D2D admission control problem, a heuristic sorting-based algorithm is proposed to index the admissible D2D links, where gain to Interference ratio （GIR） sorting criterion is used. Applying an approximate form of Shannon capacity, the power allocation problem can be solved by convex optimization and geometric programming tools efficiently. Based on the theoretical analysis, a practical algorithm is proposed. The precision can reach a trade-off between complexity and performance. Numerical simulation results confirm that combining with GIR sorting method, the proposed scheme can significantly improve the D2D system＇s capacity and fairness.