• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1527-1534
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• 2010

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.333-342
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• 2007

A nonsmooth PGD scheme for minimizing a nonsmooth convex function is presented. In the parallelization step of the algorithm, a method due to Pang, Han and Pangaraj (1991), [7], is employed to solve a subproblem for constructing search directions. The convergence analysis is given as well.

• 충청수학회지
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• 제30권1호
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• pp.31-40
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• 2017

In this paper, we consider a nonsmooth multiobjective robust optimization problem with more than two locally Lipschitz objective functions and locally Lipschitz constraint functions in the face of data uncertainty. We prove a nonsmooth sufficient optimality theorem for a weakly robust efficient solution of the problem. We formulate a Wolfe type dual problem for the problem, and establish duality theorems which hold between the problem and its Wolfe type dual problem.

• East Asian mathematical journal
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• 제35권3호
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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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• 제27권1_2호
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• pp.335-341
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• 2009

In this paper, a system of nonsmooth equations reformulated from a nonlinear complementarity problem with nonsmooth data is studied. The formulas of some subdifferentials for related functions in this system of nonsmooth equations are developed. The present work can be applied to Newton methods for solving this kind of nonlinear complementarity problem.

• 충청수학회지
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• 제37권1호
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.189-197
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• 2013

In this paper, Karush-Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible point of a nonsmooth multiobjective fractional programming problem to be an efficient or properly efficient by using generalized ($F,{\rho},{\sigma}$)-type I functions.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.539-551
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• 2005

In this paper, sufficient optimality conditions and duality results for nonsmooth vector optimization problems are given under near invexity and infineness assumptions. Also, weak vector saddle-point theorems are obtained under near invexity-infineness assumptions.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.361-367
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• 2007

In this paper we propose an implementable method for solving a nonsmooth convex optimization problem by combining Moreau-Yosida regularization, bundle and quasi-Newton ideas. The method we propose makes use of approximate subgradients of the objective function, which makes the method easier to implement. We also prove the convergence of the proposed method under some additional assumptions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.