• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1639-1650
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• 2013

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• The korean journal of orthodontics
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• v.40 no.3
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• pp.134-144
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• 2010

Objective: The aim of this study was to evaluate the volumes and areas of the upper airways in children with Class II malocclusion, using three dimensional cone-beam computed tomography (CBCT) and to compare the volumetric and cross-sectional measurements and cephalometric variables to investigate possible relationships between the upper airway and facial morphology. Methods: CBCT scans were obtained from 37 subjects (17 boys and 20 girls; average age, 11.02 years). The upper airway volumes and areas were measured, and compared with cephalometric variables. Results: The area of the PNS-posterior plane ($S_{PP}$) was significantly smaller in the Class II malocclusion group (p < 0.05). Also, the volumetric and cross-sectional measurements were lower in Class II than in Class I malocclusion groups, although the differences were not significant between the two groups (p > 0.05). The Class II malocclusion group showed significantly smaller values of PFH, mandibular body length, pog to N perp and showed larger values of FMA, ANB, and facial convexity than the Class I malocclusion group. The volume of the upper airway in front of PNS point (WN) showed negative correlation with ANB (p < 0.05). Conclusions: The Class II malocclusion group had a narrower upper airway associated with a decreased posterior facial height and a divergent growth pattern than the Class I malocclusion group.

• Imaging Science in Dentistry
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• v.42 no.4
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• pp.201-205
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• 2012

Purpose: This study was performed to assess the compatibility of cone beam computed tomography (CBCT) synthesized cephalograms with conventional cephalograms, and to find a method for obtaining normative values for three-dimensional (3D) assessments. Materials and Methods: The sample group consisted of 10 adults with normal occlusion and well-balanced faces. They were imaged using conventional and CBCT cephalograms. The CBCT cephalograms were synthesized from the CBCT data using OnDemand 3D software. Twenty-one angular and 12 linear measurements from each imaging modality were compared and analyzed using paired-t test. Results: The linear measurements between the two imaging modalities were not statistically different (p>0.05) except for the U1 to facial plane distance. The angular measurements between the two imaging modalities were not statistically different (p>0.05) with the exception of the gonial angle, ANB difference, and facial convexity. Conclusion: Two-dimensional cephalometric norms could be readily used for 3D quantitative assessment, if corrected for lateral cephalogram distortion.

• The korean journal of orthodontics
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• v.43 no.3
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• pp.113-119
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• 2013

Objective: To compare three-dimensionally the midfacial hard- and soft-tissue asymmetries between the affected and the unaffected sides and determine the relationship between the hard tissue and the overlying soft tissue in patients with nonsyndromic complete unilateral cleft lip and palate (UCLP) by cone-beam computed tomography (CBCT) analysis. Methods: The maxillofacial regions of 26 adults (18 men, 8 women) with nonsyndromic UCLP were scanned by CBCT and reconstructed by three-dimensional dental imaging. The frontal-view midfacial analysis was based on a $3{\times}3$ grid of vertical and horizontal lines and their intersecting points. Two additional points were used for assessing the dentoalveolar area. Linear and surface measurements from three reference planes (Basion-perpendicular, midsagittal reference, and Frankfurt horizontal planes) to the intersecting points were used to evaluate the anteroposterior, transverse, and vertical asymmetries as well as convexity or concavity. Results: Anteroposteriorly, the soft tissue in the nasolabial and dentoalveolar regions was significantly thicker and positioned more anteriorly on the affected side than on the unaffected side (p < 0.05). The hard tissue in the dentoalveolar region was significantly retruded on the affected side compared with the unaffected side (p < 0.05). The other midfacial regions showed no significant differences. Conclusions: With the exception of the nasolabial and dentoalveolar regions, no distinctive midfacial hard- and soft-tissue asymmetries exist between the affected and the unaffected sides in patients with nonsyndromic UCLP.