• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.905-915
• /
• 2009

Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.125-142
• /
• 2004

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius p converges to zero. This gives a justification for the use of p as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.22 no.5
• /
• pp.102-109
• /
• 1985

A new yield maximization procedure by investigating method of the multidimensional Monte Carlo integration is presented. And then maximum yield is obtained by the new modified weight selection algorithm applied to objective function of MOSFET NAND GATE Also this yield maximization procedure can be applied to nonconvex objective function.

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

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.215-224
• /
• 2019

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated.

• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.719-731
• /
• 2020

In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.

• Journal of Biomedical Engineering Research
• /
• v.36 no.5
• /
• pp.211-220
• /
• 2015

Recently, model-based iterative reconstruction (MBIR) has played an important role in transmission tomography by significantly improving the quality of reconstructed images for low-dose scans. MBIR is based on the penalized-likelihood (PL) approach, where the penalty term (also known as the regularizer) stabilizes the unstable likelihood term, thereby suppressing the noise. In this work we further improve MBIR by using a more expressive regularizer which can restore the underlying image more accurately. Here we used a spline regularizer derived from a linear combination of the two-dimensional splines with first- and second-order spatial derivatives and applied it to a non-quadratic convex penalty function. To derive a PL algorithm with the spline regularizer, we used a separable paraboloidal surrogates algorithm for convex optimization. The experimental results demonstrate that our regularization method improves reconstruction accuracy in terms of both regional percentage error and contrast recovery coefficient by restoring smooth edges as well as sharp edges more accurately.

• Management Science and Financial Engineering
• /
• v.22 no.1
• /
• pp.5-12
• /
• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

• Interaction and multiscale mechanics
• /
• v.6 no.2
• /
• pp.137-156
• /
• 2013

In this paper, a meshfree shell adaptive procedure is developed for the applications in the sheet metal forming simulation. The meshfree shell formulation is based on the first-order shear deformable shell theory and utilizes the degenerated continuum and updated Lagrangian approach for the nonlinear analysis. For the sheet metal forming simulation, an h-type adaptivity based on the meshfree background cells is considered and a geometric error indicator is adopted. The enriched nodes in adaptivity are added to the centroids of the adaptive cells and their shape functions are computed using a first-order generalized meshfree (GMF) convex approximation. The GMF convex approximation provides a smooth and non-negative shape function that vanishes at the boundary, thus the enriched nodes have no influence outside the adapted cells and only the shape functions within the adaptive cells need to be re-computed. Based on this concept, a multi-level refinement procedure is developed which does not require the constraint equations to enforce the compatibility. With this approach the adaptive solution maintains the order of meshfree approximation with least computational cost. Two numerical examples are presented to demonstrate the performance of the proposed method in the adaptive shell analysis.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.10C
• /
• pp.1402-1413
• /
• 2004

In non-rigid image registration, the Jacobian determinant of the estimated deformation should be positive everywhere since physical deformations are always invertible. We propose a constrained optimization technique at ensures the positiveness of Jacobian determinant for cubic B-spline based deformation. We derived sufficient conditions for positive Jacobian determinant by bounding the differences of consecutive coefficients. The parameter set that satisfies the conditions is convex; it is the intersection of simple half spaces. We solve the optimization problem using a gradient projection method with Dykstra's cyclic projection algorithm. Analytical results, simulations and experimental results with inhale/exhale CT images with comparison to other methods are presented.