Redundancy in Mathematical Programming

Karwan, Mark H.; Lotfi, Vahid; Zionts, Stanley; Telgen, Jan

doi:10.1007/978-3-642-45535-3

Cited by 101 publications

(75 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Worst case complexity is non-polynomial but, like the simplex algorithm, it typically visits only a fraction of the extreme points. Our implementation takes advantage of the sparse structure of the constraints, and deals with redundancy and degeneracy using the techniques of [9].…”

Section: Minimizing Linearly Constrained Concave Functionsmentioning

confidence: 99%

Maximizing Rigidity: Optimal Matching under Scaled-Orthography

Maciel

Costeira

2002

Computer Vision — ECCV 2002

View full text Add to dashboard Cite

Abstract. Establishing point correspondences between images is a key step for 3D-shape computation. Nevertheless, shape extraction and point correspondence are treated, usually, as two different computational processes. We propose a new method for solving the correspondence problem between points of a fully uncalibrated scaled-orthographic image sequence. Among all possible point selections and permutations, our method chooses the one that minimizes the fourth singular value of the observation matrix in the factorization method. This way, correspondences are set such that shape and motion computation are optimal. Furthermore, we show this is an optimal criterion under bounded noise conditions. Also, our formulation takes feature selection and outlier rejection into account, in a compact and integrated way. The resulting combinatorial problem is cast as a concave minimization problem that can be efficiently solved. Experiments show the practical validity of the assumptions and the overall performance of the method.

show abstract

Section: Minimizing Linearly Constrained Concave Functionsmentioning

confidence: 99%

Maximizing Rigidity: Optimal Matching under Scaled-Orthography

Maciel

Costeira

2002

Computer Vision — ECCV 2002

View full text Add to dashboard Cite

show abstract

“…In fact, there is a wide literature on the detection and elimination of redundant constraints in LP models [1][2][3][4][5][6][7][8][9][10][11]. Heuristic approach [13] is using an intercept matrix to identify redundant constraints prior to the start of the solution process.…”

Section: Introductionmentioning

confidence: 99%

Artificial Neural Network Based Hybrid Algorithmic Structure for Solving Linear Programming Problems

Babu¹,

Palaniappan²

2010

IJCEE

View full text Add to dashboard Cite

show abstract

“…Redundant constraints and other types of superfluous constraints are the cause of troubles in the numerical treatment of linear optimization problems, at least in the case |T | < ∞ (see Karwan et al (1983)). In order to define the relevant concepts in this paper we associate with each c ∈ R …”

mentioning

confidence: 99%

“…The concept of saturation was introduced by Boot (1962), for problems with a unique solution, whereas weak and strong saturation were defined and analyzed by Mauri (1975) and by Karwan et al (1983), assuming that |T | < ∞ and s is nonredundant, and by Goberna et al (2003a) in the general case. In the last paper, it has been proved (in Proposition 4.1) that, if s is nonsaturated (weakly saturated), then it is superfluous in the sense that…”

mentioning

confidence: 99%