arXiv subjects

Md Abu Talhamainuddin Ansary

Publications and source records attributed to Md Abu Talhamainuddin Ansary.

10 recordsLinked to original sources

arXiv2026

Adaptive Variance-Reduced Stochastic Sequential (Quadratic Constrained) Quadratic Programming

In this paper, we propose an adaptive variance-reduced stochastic sequential (quadratic constrained) quadratic programming (AVR-SS(QC)QP) method for nonlinear constrained optimization. The framework integrates SPIDER-based variance reduction, stochastic quasi-Newton curvature information, merit-function globalization, and adaptive switching between stochastic SQP and SQCQP models. The switching mechanism is governed by a relative constraint model curvature indicator that measures the second-order constraint information neglected by the linearized SQP model. A smoothed hysteresis rule ac?tivates the SQCQP model only when the relative constraint curvature is significant. An exact L1 merit function with Armijo backtracking globalizes the resulting directions, while a coupled stochastic Lyapunov analysis controls the interaction between gradient-estimation error and optimization progress. Under standard smoothness, sampling, regularity, and second-order conditions, we establish almost-sure consistency of the variance-reduced gradient estimator and global convergence of the KKT residual. We further show that, near regular KKT points, the curvature indicator vanishes and the method eventually selects the computationally cheaper SQP model. Numerical experiments on a sparse principal component analysis problem illustrate the practical be?havior of the proposed framework.

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arXiv2026

A Novel Fractional-Order Accelerated Gradient Descent Method for Nonlinear Optimization with Application to Posture Recognition

This article proposes a Caputo fractional accelerated gradient descent (CFAGD) method for unconstrained optimization problems that is applicable to both smooth and a class of non-smooth objective functions. The proposed approach incorporates an adaptive (\b{eta}k)-parameter, which is heuristically updated throughout the iterative process to improve the search direction. Furthermore, the method employs the Caputo fractional derivative together with the adaptive (\b{eta}^k)-parameter, thereby preserving the memory characteristics associated with non-integer-order derivatives. A suitable step-size is selected via an inexact line-search technique based on the Armijo condition. The central idea is to scale the step-size by a positive parameter to improve the behavior of the iterates as they approach an optimal point, thereby generating a descent sequence. Under strong convexity and bounded Hessian assumptions, linear convergence of the proposed method is established. Numerical validations, including neural-network-based examples, further indicate that the CFAGD method can achieve faster and more stable performance than competing approaches.

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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 Conjugate Gradient Method for Nonlinear Programming Problems using Caputo Fractional Gradients

The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo fractional derivative that provides integer-order derivatives information. A descent direction is obtained using the Caputo fractional gradients of two consecutive iterative points with a parameter ($β$). An inexact line search technique based on Armijo-Wolfe line conditions is used to find a suitable step length. Finally, a descent sequence is generated. The convergence results are derived under mild assumptions that ensuring of convergence is at least linear. Moreover, the convergence of the proposed method for quadratic functions is established through a Tikhonov-regularized formulation that can be interpreted as an extension of the least-squares approach. Finally, some numerical experiments, including neural network applications, are performed to justify that the proposed method achieves faster and more stable performance.

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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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arXiv2025

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems

This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth multi-objective optimization problems. Moreover, the proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At every iteration of the proposed method, a subproblem is solved to identify a suitable descent direction toward an optimal solution. This subproblem involves an adaptive-order Caputo fractional gradient for each objective function. An Armijo-type line search is applied to determine a suitable step length. The convergence of this method for the Tikhonov-regularized solution is justified under mild assumptions. The proposed method is verified using different numerical problems, including neural networks.

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arXiv2024

A Trust Region Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a sub problem is solved to find a suitable direction. This sub problem uses a quadratic approximation of each smooth function and a trust region constraint. An update formula for trust region radius is introduce in this paper. A sequence is generated using descent directions. It is justified that under some mild assumptions every accumulation point of this sequence is a critical point. The proposed method is verified and compared with some existing methods using a set of problems.

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arXiv2022

A Newton-Type Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method deals with unconstrained convex multi-objective optimization problems. This method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a suitable descent direction. The subproblem uses a quadratic approximation of each smooth function. An Armijo type line search is conducted to find a suitable step length. A sequence is generated using the descent direction and step length. The Global convergence of this method is justified under some mild assumptions. The proposed method is verified and compared with some existing methods using a set of problems.

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arXiv2020

A Sequential Quadratic Programming Method for Constrained Multi-objective Optimization Problems

In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear approximation of all objective functions as well as constraint functions. The sub-problem at every iteration of the sequence has feasible solution. A non-differentiable penalty function is used to deal with constraint violations. A descent sequence is generated which converges to a critical point under the Mangasarian-Fromovitz constraint qualification along with some other mild assumptions. The method is compared with a selection of existing methods on a suitable set of test problems.

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