scholarly journals A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Mio Horai ◽  
Hideo Kobayashi ◽  
Takashi G. Nitta
Keyword(s):  
Global Optimization ◽  
Global Convergence ◽  
Nonlinear Optimization ◽  
Branch And Bound ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
New Method ◽  
Linear Relaxation ◽  
Global Optimization Problem ◽  
Nonconvex Global Optimization

We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

scholarly journals Global Optimization for the Sum of Certain Nonlinear Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mio Horai ◽  
Hideo Kobayashi ◽  
Takashi G. Nitta
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Global Optimization Problem ◽  
Nonlinear Functions ◽  
Nonconvex Optimization Problems ◽  
Second Derivatives ◽  
Fractional Function

We extend work by Pei-Ping and Gui-Xia, 2007, to a global optimization problem for more general functions. Pei-Ping and Gui-Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei-Ping and Gui-Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm.

scholarly journals Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Numerical Test ◽  
Function Approach ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Filled Function ◽  
Global Minima ◽  
Smooth Case ◽  
Definition Of

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

An improved teaching–learning-based optimization algorithm for solving global optimization problem

2015 ◽  
Vol 297 ◽  
pp. 171-190 ◽  
Author(s):  
Debao Chen ◽  
Feng Zou ◽  
Zheng Li ◽  
Jiangtao Wang ◽  
Suwen Li
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Global Optimization Problem ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning

scholarly journals Using a vision cognitive algorithm to schedule virtual machines

2014 ◽  
Vol 24 (3) ◽  
pp. 535-550 ◽  
Author(s):  
Jiaqi Zhao ◽  
Yousri Mhedheb ◽  
Jie Tao ◽  
Foued Jrad ◽  
Qinghuai Liu ◽  
...  
Keyword(s):  
Global Optimization ◽  
Energy Consumption ◽  
Virtual Machine ◽  
Optimization Problem ◽  
Virtual Machines ◽  
Scheduling Algorithm ◽  
Primary Concern ◽  
Global Optimization Problem ◽  
Vm Scheduling ◽  
Operation Cost

Abstract Scheduling virtual machines is a major research topic for cloud computing, because it directly influences the performance, the operation cost and the quality of services. A large cloud center is normally equipped with several hundred thousand physical machines. The mission of the scheduler is to select the best one to host a virtual machine. This is an NPhard global optimization problem with grand challenges for researchers. This work studies the Virtual Machine (VM) scheduling problem on the cloud. Our primary concern with VM scheduling is the energy consumption, because the largest part of a cloud center operation cost goes to the kilowatts used. We designed a scheduling algorithm that allocates an incoming virtual machine instance on the host machine, which results in the lowest energy consumption of the entire system. More specifically, we developed a new algorithm, called vision cognition, to solve the global optimization problem. This algorithm is inspired by the observation of how human eyes see directly the smallest/largest item without comparing them pairwisely. We theoretically proved that the algorithm works correctly and converges fast. Practically, we validated the novel algorithm, together with the scheduling concept, using a simulation approach. The adopted cloud simulator models different cloud infrastructures with various properties and detailed runtime information that can usually not be acquired from real clouds. The experimental results demonstrate the benefit of our approach in terms of reducing the cloud center energy consumption

On variational aspects of some nonconvex nonsmooth global optimization problem

1995 ◽  
Vol 6 (4) ◽  
pp. 383-400 ◽  
Author(s):  
Z. Naniewicz
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Global Optimization Problem

scholarly journals On Complexity of a Global Optimization Problem

2003 ◽  
Vol 8 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Urfat Nuriyev
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Global Optimization Problem
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