• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.139-147
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• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.65-70
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• 2021

We characterize the solution set for a second-order cone linear fractional optimization problem (P). We present sequential Lagrange multiplier characterizations of the solution set for the problem (P) in terms of sequential Lagrange multipliers of a known solution of (P).

• East Asian mathematical journal
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• v.35 no.3
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.853-867
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• 2013

In this paper a methodology is developed to solve a nonlinear fractional programming problem, whose objective function and constraints are interval valued functions. Interval valued convex fractional programming problem is studied. This model is transformed to a general convex programming problem and relation between the original problem and the transformed problem is established. These theoretical developments are illustrated through a numerical example.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.465-475
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• 2016

We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1535-1544
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• 2010

Sufficient optimality conditions for a class of generalized non-differentiable fractional optimization programming problems are established. Moreover, we prove the weak and strong duality theorems under (V, $\rho$)-invexity assumption.

• Management Science and Financial Engineering
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• v.12 no.1
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• pp.113-125
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• 2006

Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.19-32
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• 2005

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.