2015
DOI: 10.1177/1081286514566704
|View full text |Cite|
|
Sign up to set email alerts
|

RETRACTED: Double well potential function and its optimization in the n-dimensional real space: part I

Abstract: A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. When the function is bounded from below, it has a very unique property that two or more local minimum solutions are separated by one local maximum solution, or one saddle point. Our intension in this paper is to categorize all possible configurations of the double well potential functions mathematically. In part Numerical examples are provided to illustrate the important features of the problem and th… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
13
0

Year Published

2015
2015
2023
2023

Publication Types

Select...
3
2
1

Relationship

4
2

Authors

Journals

citations
Cited by 9 publications
(13 citation statements)
references
References 12 publications
0
13
0
Order By: Relevance
“…A similar argument applies for any other components. h The next result shows that the sufficient condition 1 2 k w à k 2 À n + a 1 ! 0 in Lemma 3 is indeed necessary for a critical point to become the global minimizer.…”
Section: Characterization Of the Global Minimizermentioning
confidence: 84%
See 2 more Smart Citations
“…A similar argument applies for any other components. h The next result shows that the sufficient condition 1 2 k w à k 2 À n + a 1 ! 0 in Lemma 3 is indeed necessary for a critical point to become the global minimizer.…”
Section: Characterization Of the Global Minimizermentioning
confidence: 84%
“…For simplicity, we define n = À 1 2 c T (I À B(B T B) À1 B T )c + d and c = P T f À DP T B T c. By dropping the constant terms, we can rewrite problem (DWP) defined in (1) Recall that the canonical primal problem defined in (19) of part I is to minimize…”
Section: Characterization Of a Local Nonglobal Minimizermentioning
confidence: 99%
See 1 more Smart Citation
“…The special case (3-RS) is the wellknown Nestrov-Polyak subproblem [21], which is an important subproblem in regularized Newton methods for unconstrained optimization. The double-well potential minimization problem [22] corresponds to (4-RS). If A 0, h(x) is convex as p > 2.…”
Section: Generalized P-regularized Subproblem With P >mentioning
confidence: 99%
“…As a consequence, both (QP1EQC) and (GTRS) are completely analyzed. We remark that (QP1EQC) itself has many interesting applications, including the double well potential optimization problem [10,35], the time of arrival geolocation problem [15] and unbiased least squares optimization for system identification [26]. In particular, the double well potential model came from numerical approximations to the generalized Ginzburg-Landau functionals [18].…”
Section: S-condition 2([3] Thm A2)mentioning
confidence: 99%