Solving Multi-Object Programming Problems by Homotopy Inner Point Method under Quasi-Normal Cone Condition

2011 ◽  
pp. 1-6
Author(s):  
He Li ◽  
Wang Xiu-yu ◽  
Jin Jian lu ◽  
Liu Qing huai
Keyword(s):  
Normal Cone ◽  
Point Method ◽  
Cone Condition

Data Processing with Combined Homotopy Methods for a Class of Nonconvex Optimization Problems

2014 ◽  
Vol 1046 ◽  
pp. 403-406 ◽  
Author(s):  
Yun Feng Gao ◽  
Ning Xu
Keyword(s):  
Data Processing ◽  
Nonconvex Optimization ◽  
Normal Cone ◽  
Optimization Problems ◽  
Feasible Region ◽  
Specific Class ◽  
Homotopy Methods ◽  
Cone Condition ◽  
Nonconvex Optimization Problems ◽  
Theoretical Results

On the existing theoretical results, this paper studies the realization of combined homotopy methods on optimization problems in a specific class of nonconvex constrained region. Contraposing to this nonconvex constrained region, we give the structure method of the quasi-normal, prove that the chosen mappings on constrained grads are positive independent and the feasible region on SLM satisfies the quasi-normal cone condition. And we construct combined homotopy equation under the quasi-normal cone condition with numerical value and examples, and get a preferable result by data processing.

Aggregate Homotopy Method for Min-Max-Min Programming Satisfying a Weak-Normal Cone Condition

2011 ◽  
Vol 50-51 ◽  
pp. 669-672
Author(s):  
Hui Juan Xiong ◽  
B. Yu
Keyword(s):  
Data Mining ◽  
Support Vector Machine ◽  
Normal Cone ◽  
Support Vector Machine Model ◽  
Homotopy Method ◽  
Support Vector ◽  
Cone Condition ◽  
Machine Model ◽  
Nonsmooth Programming

Min-max-min programming is an important but difficult nonsmooth programming. An aggregate homotopy method was given for solving min-max-min programming by Bo Yu el al. However, the method requires a difficult to verify weak-normal cone condition. Moreover, the method is only theoretically with no algorithmic implementation. In this paper, the weak normal cone condition is discussed first. A class of min-max-min programming satisfying the condition is introduced. A detailed algorithm to implement the method is presented. Models arising from some applications such as support vector machine for multiple-instance classification in data mining, can be included in the problem. In the end, the aggregate homotopy method is given to solve the multiple-instance support vector machine model.

Aggregate Constraint Homotopy Method for Nonlinear Programming on Unbounded Set

2011 ◽  
Vol 50-51 ◽  
pp. 283-287
Author(s):  
Yu Xiao ◽  
Hui Juan Xiong ◽  
Zhi Gang Yan
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Additional Assumption ◽  
Normal Cone ◽  
Constraint Qualifications ◽  
Convergence Result ◽  
Homotopy Method ◽  
Cone Condition ◽  
Feasible Set

In [1], an aggregate constraint aggregate (ACH) method for nonconvex nonlinear programming problems was presented and global convergence result was obtained when the feasible set is bounded and satisfies a weak normal cone condition with some standard constraint qualifications. In this paper, without assuming the boundedness of feasible set, the global convergence of ACH method is proven under a suitable additional assumption.

scholarly journals A Comparison of Normal Cone Conditions for Homotopy Methods for Solving Inequality Constrained Nonlinear Programming Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhengyong Zhou ◽  
Ting Zhang
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Constraint Qualification ◽  
Normal Cone ◽  
Homotopy Methods ◽  
Cone Condition ◽  
Feasible Set ◽  
Constrained Nonlinear Programming ◽  
Cone Conditions

Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.

The Combined Homotopy Methods for Optimizition under the Quasi-Normal Cone Condition

2012 ◽  
Vol 459 ◽  
pp. 16-18
Author(s):  
Yun Feng Gao
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Research Field ◽  
Point Method ◽  
Convex Programming Problem ◽  
Cone Condition ◽  
Reverse Convex ◽  
Theoretical Results

Non-convex programming problem is a hot problem in research field of optimization problems, since the interior point method is applied for solving programming problem. In this paper, we use the homotopy interior point method for solving a class of optimization problems by the existing theoretical results under quasi-norm cone condition. Contrary to this partial reverse convex constrained domain, we give the structure method of the quasi-norm cone condition, construct the combined homotopy method under quasi-norm cone condition and show some numerical examples

Scanning Electron Microscopy of Dried and Acid Treated Shells of Difflugia

1973 ◽  
Vol 31 ◽  
pp. 448-449
Author(s):  
Barry S. Eckert ◽  
S. M. McGee-Russell
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Critical Point ◽  
Point Method ◽  
External Structure ◽  
Cell Locomotion ◽  
Single Opening ◽  
Scanning Electron

Difflugia lobostoma is a shelled amoeba. The shell is an external structure of considerable mass which presents the animal with special restrictions in cell locomotion which are met by the development of active pseudopodial lobopodia containing, apparently, an organized system of thick and thin microfilaments (Eckert and McGee-Russell, 1972). The shell is constructed of sand grains picked up from the environment, and cemented into place with a secretion. There is a single opening through which lobopods extend. The organization of the shell was studied by scanning electron microscopy (SEM).Intact shells or animals with shells were dried by the critical point method of Anderson (1966) or air dried, after primary fixation in glutaraldehyde.

Dermoscopy Analysis Easy by Three-Point Method

2007 ◽  
Vol 38 (3) ◽  
pp. 62
Author(s):  
SHERRY BOSCHERT
Keyword(s):  
Point Method
Sign in / Sign up

Export Citation Format

Share Document