• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.261-275
• /
• 2003

In this paper we study two stage problems of stochastic convex programming. Solving the problems is very hard. A L-shaped method for it is given. The implement of the algorithm is simple, so less computation work is needed. The result of computation shows that the algorithm is effective.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.379-390
• /
• 2005

In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.68 no.1
• /
• pp.159-166
• /
• 2019

Due to the various engagement situations, it is very difficult to generate the optimal trajectory with several constraints. This paper investigates the sequential convex programming for the impact angle control with the additional constraint of altitude limit. Recently, the SOCP(Second-Order Cone Programming), which is one area of the convex optimization, is widely used to solve variable optimal problems because it is robust to initial values, and resolves problems quickly and reliably. The trajectory optimization problem is reconstructed as convex optimization problem using appropriate linearization and discretization. Finally, simulation results are compared with analytic result and nonlinear optimization result for verification.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.419-423
• /
• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• Structural Engineering and Mechanics
• /
• v.18 no.4
• /
• pp.461-474
• /
• 2004

A proposed incremental model for the solution of a general class of convex programming problems is introduced. The model is an extension of that developed by Mahmoud et al. (1993) which is limited to linear constraints having nonzero free coefficients. In the present model, this limitation is relaxed, and allowed to be zero. The model is extended to accommodate those constraints of zero free coefficients. The proposed model is applied to solve the elasto-static contact problems as a class of variation inequality problems of convex nature. A set of different physical nature verification examples is solved and discussed in this paper.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.227-235
• /
• 2004

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

• Structural Engineering and Mechanics
• /
• v.23 no.4
• /
• pp.431-447
• /
• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.501-505
• /
• 1998

In this paper, an LP problem with convex polyhedral objective coefficients is treated. In the problem, the interactivities of the uncertain objective coefficients are represented by a bounded convex polyhedron (a convex polytope). We develop a computation algorithm of a maxmin achievement rate solution. To solve the problem, first, we introduce the relaxation procedure. In the algorithm, a sub-problem, a bilevel programing problem, should be solved. To solve the sub-problem, we develop a solution method based on a branch and bound method. As a result, it is shown that the problem can be solved by the repetitional use of the simplex method.

• International Journal of Control, Automation, and Systems
• /
• v.1 no.3
• /
• pp.271-281
• /
• 2003

In this paper, a new nonlinear programming approach is suggested to solve biaffine matrix inequality (BMI) problems in multiobjective and structured controls. It is shown that these BMI problems are reduced to nonlinear minimization problems. An algorithm that is easily implemented with existing convex optimization codes is presented for the nonlinear minimization problem. The efficiency of the proposed algorithm is illustrated by numerical examples.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.21 no.1
• /
• pp.1-17
• /
• 1996

There have been considerable researches for solving large-scale separable convex optimization ptoblems. In this paper we present a method for large-scale nonseparable smooth convex optimization problems with block-angular linear constraints. One of them is occurred in reconfiguration of the virtual path network which finds the routing path and assigns the bandwidth of the path for each traffic class in ATM (Asynchronous Transfer Mode) network [1]. The solution is approximated by solving a sequence of the block-angular structured separable quadratic programming problems. Bundle-based decomposition method [10, 11, 12]is applied to each large-scale separable quadratic programming problem. We implement the method and present some computational experiences.