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Nimit Nimana

Publications and source records attributed to Nimit Nimana.

8 recordsLinked to original sources
arXiv2026

Fixed-Point Delayed Subgradient Methods for Nonsmooth Convex Optimization Problems

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid steepest descent method and the idea of a delayed subgradient scheme in which allows the use of staled subgradients from the earlier iteration when updating the next iteration. We start the convergence part by deriving an upper bound for the difference of the best-achieved function values and the optimal value. After that, to ensure the convergence in iterations, we prove that there exists a subsequence of the generated sequence by the proposed method which converges to an optimal solution. Moreover, we subsequently show that the whole generated sequence converges to an optimal solution when the strict convexity of the objective function is imposed. We further extend the presented results to the centralized network system consisting of a finite number of workers and a central server. Finally, we apply the proposed method to image inpainting problems. The numerical results describe the effect of delay in many cases of objective functions.

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arXiv2026

Federated Incremental Subgradient Method for Convex Bilevel Optimization Problems

In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in situations where the inner-level problem does not have a unique solution. This has led to the idea of introducing an outer-level objective function to select a solution with the specific desired properties. We propose an iterative method that combines an incremental algorithm with a broadcast algorithm, both based on the principles of federated learning. Under appropriate assumptions, we establish the convergence results of the proposed algorithm. To demonstrate its performance, we present two numerical examples related to binary classification and a location problem.

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arXiv2025

Subgradient Splitting Methods for Nonsmooth Fractional Programming with Fixed-Point Constraints

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient steps separately for the convex numerator and the concave denominator. These methods offer a straightforward approach by eliminating the need to solve subproblems at each iteration. By leveraging fixed-point constraints, the proposed algorithms are particularly well-suited for problems with complex constraint structures. Under certain assumptions, we establish the convergence of the proposed methods. Furthermore, to address large-scale optimization, we propose an incremental subgradient algorithm for a class of nonsmooth sum-of-ratios fractional programming problems and analyze its convergence. Finally, we present numerical experiments, including comparative analyses of our algorithms with existing methods, to demonstrate the effectiveness and performance of the proposed approach.

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arXiv2020

Extrapolated Sequential Constraint Method for Variational Inequality over the Intersection of Fixed-Point Sets

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each iteration, the proposed method is updated based on the ideas of a hybrid conjugate gradient method used to accelerate the well-known hybrid steepest descent method, and an extrapolated cyclic cutter method for solving a common fixed point problem. We prove strong convergence of the method under some suitable assumptions of step-size sequences. We finally show the numerical efficiency of the proposed method compared to some existing methods.

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arXiv2020

Incremental proximal gradient scheme with penalization for constrained composite convex optimization problems

We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with smooth penalization technique is proposed. We show the convergence of the generated sequence of iterates to an optimal solution of the optimization problems, provided that a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. Finally, the functionality of the method is illustrated by some numerical experiments addressing image inpainting problems and generalized Heron problems with least squares constraints.

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arXiv2020

Star subgradient projection for solving quasi-convex feasibility problems

In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence result of the considered method by using properties of the introduced nonlinear operator.

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arXiv2018

Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximal monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided the condition corresponded to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.

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