KKU - Math. Optimization

NIMIT NIMANA
Associate Professor in Mathematics
Department of Mathematics, Faculty of Science, Khon Kaen University

News:

📝 November 18, 2025 – The paper "Federated Incremental Subgradient Method for Convex Bilevel Optimization Problems" (authors: Boontawee, S., Prangprakhon, M., & Nimana, N.) is accepted for publication in IEEE Control Systems Letters.
🛬 🇹🇼 October, 26 - 27 2025 – Prof. Jein-Shan Chen from National Taiwan Normal University (NTNU), Taiwan, visits us and delivers a special lecture titled “Smoothing Functions for Sparse Optimisation: A Unified Framework” at our department. NEWS
🛫 🇯🇵 September 14 - November 27, 2025 – Jedsadapong Pio-on is visiting the Akita Prefectural University, Akita, Japan, hosted by Prof. Shin-ya Matsushita.
📝 August 7, 2025 – The paper "A Simultaneous Quasi-Subgradient Method for Minimizing Convex Function with Quasi-Convex Functional Constraints" (authors: Pio-on, J., & Nimana, N.) is accepted for publication in Journal of Optimization Theory and Applications.
📝 July 24, 2025 – The paper "Delayed Star Subgradient Methods for Constrained Nondifferentiable Quasi-Convex Optimization" (authors: Pankoon, O., & Nimana, N.) is accepted for publication in Algorithms.
🛫 🇵🇭 July 14–22, 2025 – Nimit Nimana gives the invited lecture series on Optimization for Data-Driven Research at the 2025 SEAMS School Los Baños, Theoretical and Computational Tools for the Data-Enabled Sciences organized at the Institute of Mathematical Sciences, College of Arts and Sciences, University of the Philippines Los Banos, Laguna, Philippines.
👏 June 20, 2025 – Ontima Pankoon successfully defends her Master's thesis "Delayed subgradient methods for nonsmooth optimizations with fixed- point constraints".
🛫 🇹🇼 June 3, 2025 – Tipsuda Arunrat gives the invited lecture on An Iterative Regularized Subgradient Algorithm with Information Delay for Solving Bilevel Convex Optimization Problems at the Mini Optimization Workshop organized by Prof. Jein-Shan Chen at the Department of Mathematics, National Taiwan Normal University, Taiwan.
🛫 🇹🇼 June 3, 2025 – Nimit Nimana gives the invited lecture on Simultaneous Quasi-Subgradient Method for Minimizing Convex Functions with Quasi-Convex Functional Constraints at the Mini Optimization Workshop organized by Prof. Jein-Shan Chen at the Department of Mathematics, National Taiwan Normal University, Taiwan.
🛫 🇹🇼 June 1–14, 2025 – Nimit Nimana and Tipsuda Arunrat visit the Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, hosted by Prof. Jen-Chin Yao.
👏 May 6, 2025 – Mootta Prangprakhom successfully defends her PhD dissertation "Iterative methods for solving nonlinear fractional optimization problems".
📝 February 22, 2025 – The paper "A Greedy Fixed-Point Method for Solving Variational Inequalities over the Fixed-Point Constraints" (authors: Prangprakhon, M., Pioon, J., Nimana, N., & Cho, Y. J.) is accepted for publication in Numerical Functional Analysis and Optimization.
📝 February 20, 2025 – The paper "Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex-Concave Minimax Optimization" (authors: Feesantia, T., Arunrat, T., Nimana, N.) is accepted for publication in Algorithms.
🛫 🇵🇱 October 14 – November 15, 2024 – Nimit Nimana visits the Institute of Mathematics, University of Zielona Góra, Zielona Góra, Poland. His visit is hosted by Prof. Andrzej Cegielski.

Preprint Updates:

Subgradient Splitting Methods for Nonsmooth Fractional Programming with Fixed-Point ConstraintsWe 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.

Federated Incremental Subgradient Method for Convex Bilevel Optimization ProblemsIn 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.

Recent Publications:

Federated Incremental Subgradient Method for Convex Bilevel Optimization ProblemsIn 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.

A Simultaneous Quasi-Subgradient Method for Minimizing Convex Function with Quasi-Convex Functional Constraints - Journal of Optimization Theory and ApplicationsIn this work, we consider a convex minimization problem over the intersection of a compact convex simple set and a finite intersection of sublevel sets of quasi-convex functions. We propose the quasi-subgradient type method which separately deals with the objective function and a simple constrained set through a subgradient projection scheme and then performs parallel feasibility updates of constrained functions via a quasi-subgradient scheme with the appropriate weight function. This strategy provides a straightforward computation since we need not solve a subproblem to determine the metric projection onto the whole constrained set. Focusing on the convergence results, we prove subsequence convergence to the optimal solution of the considered problem and also establish the convergence rate for functional value to the optimal value. Additionally, by imposing the Hölder error bound property, we prove the convergence of the whole sequences to the optimal solution. We finally perform a numerical example to demonstrate the convergence behaviors of the proposed method for various choices of relating parameters and weight functions.

NIMIT NIMANAAssociate Professor in MathematicsDepartment of Mathematics, Faculty of Science, Khon Kaen University

News:

Preprint Updates:

Recent Publications:

Contact Information:Room SC 7316 Building SC 07 Department of MathematicsFaculty of ScienceKhon Kaen UniversityKhon Kaen, 40002, THAILANDnimitni@kku.ac.th

NIMIT NIMANA
Associate Professor in Mathematics
Department of Mathematics, Faculty of Science, Khon Kaen University

Contact Information:
Room SC 7316 Building SC 07
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
nimitni@kku.ac.th