Enumerative methods in nonconvex programming

An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives

Management Science ◽

10.1287/mnsc.31.7.847 ◽

1985 ◽

Vol 31 (7) ◽

pp. 847-851 ◽

Cited By ~ 14

Author(s):

R. Jagannathan

Keyword(s):

Nonconvex Programming

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A Deterministic Method for Solving the Sum of Linear Ratios Problem

Mathematical Problems in Engineering ◽

10.1155/2020/6174352 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Zhenping Wang ◽

Yonghong Zhang ◽

Paolo Manfredi

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Branch And Bound ◽

Nonconvex Programming ◽

Real Life ◽

Branch And Bound Algorithm ◽

Separation Technique ◽

Linear Programming Relaxation ◽

Deterministic Method ◽

Linearization Technique

Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.

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A Multistage Solution Approach for Dynamic Reactive Power Optimization Based on Interval Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2018/3854812 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Xiaodong Shen ◽

Yang Liu ◽

Yan Liu

Keyword(s):

Large Scale ◽

Reactive Power ◽

Power Optimization ◽

Programming Model ◽

Nonconvex Programming ◽

Interval Uncertainty ◽

Mixed Integer ◽

Reactive Power Optimization ◽

Renewable Energy Resources ◽

Integer Quadratic Programming

In order to solve the uncertainty and randomness of the output of the renewable energy resources and the load fluctuations in the reactive power optimization, this paper presents a novel approach focusing on dealing with the issues aforementioned in dynamic reactive power optimization (DRPO). The DRPO with large amounts of renewable resources can be presented by two determinate large-scale mixed integer nonlinear nonconvex programming problems using the theory of direct interval matching and the selection of the extreme value intervals. However, it has been admitted that the large-scale mixed integer nonlinear nonconvex programming is quite difficult to solve. Therefore, in order to simplify the solution, the heuristic search and variable correction approaches are employed to relax the nonconvex power flow equations to obtain a mixed integer quadratic programming model which can be solved using software packages such as CPLEX and GUROBI. The ultimate solution and the performance of the presented approach are compared to the traditional methods based on the evaluations using IEEE 14-, 118-, and 300-bus systems. The experimental results show the effectiveness of the presented approach, which potentially can be a significant tool in DRPO research.

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