arXiv subjects

Bikram Adhikary

Publications and source records attributed to Bikram Adhikary.

3 recordsLinked to original sources

arXiv2026

One-parameter Filled Function Method for Non-convex Multi-objective Optimization Problems

In this paper, a new one-parameter filled function approach is developed for nonlinear multi-objective optimization. Inspired by key filled function ideas from single-objective optimization, the proposed method is adapted to the multi-objective setting. It avoids scalarization weights and does not impose any prior preference ordering among objectives. A descent-based procedure is first applied to obtain a local weak efficient solution. An associated filled function is then constructed and used to derive another local weak efficient solution that improves upon the current one. Repeating these phases drives the search toward global weak efficiency and yields an approximation of the global Pareto front, including in non-convex problems where multiple local Pareto fronts may exist. Numerical experiments on a set of test problems demonstrate the effectiveness of the proposed approach relative to existing methods.

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arXiv2025

A Tunneling Method for Nonlinear Multi-objective Optimization Problems

In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At any critical point, an auxiliary function is developed to find a different critical point that dominates the previous one. By repeatedly applying the tunneling procedure, it is possible to construct a broader approximation to the global Pareto front in nonconvex multi-objective optimization problems that may contain multiple local Pareto fronts. An algorithm is then designed based on this auxiliary function, and the convergence of this algorithm is justified under some mild assumptions. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed method and to justify the theoretical results.

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arXiv2025

Global Descent Method for Non-convex Multi-objective Optimization Problems

In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for predefined scalars or ordering information of objective functions. Initially, the proposed method identifies a local weak efficient solution using any suitable descent algorithm, then applies an auxiliary function termed the multi-objective global descent function to systematically transition toward improved local weak efficient solutions. It is justified that this method can generate a global Pareto front for non-convex problems, which has many different local Pareto fronts. Finally, comprehensive numerical experiments on benchmark non-convex multi-objective optimization problems have been done to demonstrate the method's robustness, scalability and effectiveness of the proposed method.

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