• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.29-35
• /
• 2016

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.433-438
• /
• 2014

A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.62 no.10
• /
• pp.1349-1353
• /
• 2013

The optimal analysis has objective functions, equality constraint functions and inequality functions. Objective functions may be used with inequality function, because occasionally variables are moved to non-analytic condition with calculating objective functions. But inequality constraint functions are very complicated problem in a optimal analysis. this paper suggest a method to solve inequality constraint functions.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.2
• /
• pp.3-13
• /
• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.4
• /
• pp.720-730
• /
• 2002

Automated design of large structures requires efficient and accurate optimization algorithms because of a large number of design variables and design constraints. The objective of this study is to examine the characteristics of the Kreisselmeier -Steinhauser envelope function and to investigate va tidily of accumulating constraint functions into a small number of constraint functions or even into a single constraint function. The commercial package DOT is adopted as a local optimizer. The optimum results using the envelope function are compared with those of the conventional method for a number of numerical examples and the differences between them are shown to be negligible.

• Journal of Korean Institute of Industrial Engineers
• /
• v.22 no.2
• /
• pp.209-229
• /
• 1996

Scheduling problems which determine the sequence of jobs are one of the Important issues to many industries. This paper deals with a single-machine job sequencing problem which has complex constraints and an objective function. To solve the problem, an expressive constraint description language and an automatic code generator are developed for our scheduling system. The user just needs to describe the scheduling problem using the constraint description language that allows to express both quantitative and qualitative constraints as well as an objective function in real world semantics. Then, a complete scheduling program based on constraint satisfaction technique is automatically generated through the code generator. Advantage of this approach is that models of the scheduling problems are easily developed and maintained because models ore formulated by using the language which reflects real world semantics.

• Journal of Power System Engineering
• /
• v.14 no.3
• /
• pp.33-38
• /
• 2010

Technology of vehicle industry has been developing and it is required a better vehicle performance than before. Therefore, the consumers are asking not only an economic efficiency, functionality, polished design, ride comfort and silence but also a driving stability. The ride comfort, silence and driving stability are influenced by the size of vehicle and various facilities. But the principal factor is a room noise and vibration sensed by a driver and passenger. Thus, the NVH of vehicle has been raised and used as a principal factor for evaluation of vehicle performance. The primary objective of this study is an optimized design of powertrain mounting system. To optimized design was applied MSC.Nastran optimization modules. Results of dynamic analysis for powertrain mounting system was investigated. By theses results, design variables was applied 12 dynamic spring constant. And the weighting factor according to translational displacement and rotational displacement applied 3 cases. The objective function was applied to minimize displacement of powertrain. And the design variable constraint was imposed dynamic spring constant ratio. The constraint of design variable for objective function was imposed bounce displacement for powertrain.

• Bulletin of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.141-148
• /
• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.12 s.243
• /
• pp.1629-1637
• /
• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• Architectural research
• /
• v.11 no.1
• /
• pp.15-23
• /
• 2009

An application of the constrained adaptive topology optimization (CATO) algorithm is described for three-dimensional topology optimization of engineering structures. The enhanced assumed strain lower order solid finite element (FE) is used to evaluate the values of objective and constraint functions required in optimization process. The strain energy (SE) terms such as elastic and modal SEs are employed as the objective function to be minimized and the initial volume of structures is introduced as the constraint function. The SIMP model is adopted to facilitate the material redistribution and also to produce clearer and more distinct structural topologies. The linearly weighted objective function is introduced to consider both static and dynamic characteristics of structures. Several numerical tests are tackled and it is used to investigate the performance of the proposed three-dimensional topology optimization process. From numerical results, it is found to be that the CATO algorithm is easy to implement and extremely applicable to produce the reasonable optimum topologies for three dimensional optimization problems.