arXiv subjects

Tapas Mondal

Publications and source records attributed to Tapas Mondal.

5 recordsLinked to original sources

arXiv2026

PRP, HS and LS Conjugate Gradient Methods for Interval-Valued Multiobjective Optimization Problems

In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story schemes for computing Pareto critical points in unconstrained interval-valued multiobjective optimization problems. The proposed algorithm incorporates a Wolfe line search strategy to determine a suitable range of step size that satisfies the standard Wolfe conditions. For each of the proposed variants of the nonlinear conjugate gradient method, we establish rigorous global convergence results under appropriate assumptions. To demonstrate the effectiveness of the proposed methods, we conduct numerical experiments on a set of benchmark test problems and present a comprehensive performance profile analysis.

math.OC↗

arXiv2026

Nonlinear Conjugate Gradient Method for Multiobjective Optimization Problems of Interval-Valued Maps

In this article, we propose an algorithm for the nonlinear conjugate gradient method to find a Pareto critical point of unconstrained multiobjective interval optimization problems. In this algorithm, we use the Wolfe line search procedure to find the step length. After defining the standard Wolfe conditions and the strong Wolfe conditions, we prove that there exists an interval of the step length that satisfies the standard Wolfe conditions and the strong Wolfe conditions. Further, to study the convergence analysis of our proposed algorithm, we derive the result related to the Zoutendijk condition. In the convergence analysis, first, we prove the global convergence property of our proposed algorithm for a general conjugate gradient algorithmic parameter. Further, we consider four variants of the conjugate gradient algorithmic parameter, such as Fletcher-Reeves, conjugate descent, Dai-Yuan, and modified Dai-Yuan. For each variant of the algorithmic parameter, we prove the global convergence results of our proposed algorithm. Finally, we test our algorithm on some test problems and make a performance profile.

math.OC↗

arXiv2026

Newton Method for Multiobjective Optimization Problems of Interval-Valued Maps

In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs. Introducing this relationship, we develop an algorithm aimed at computing a Pareto critical point. The algorithm incorporates the computation of a descent direction at a non-Pareto critical point and employs an Armijo-like line search strategy to ensure sufficient decrease. Under suitable assumptions, we prove that the sequence generated by our proposed algorithm converges to a Pareto critical point. The effectiveness and performance of the proposed method are demonstrated through a series of numerical experiments on some test problems. Finally, we apply our proposed algorithm in a portfolio optimization problem with interval uncertainty.

math.OC↗

arXiv2023

Uncertain random geometric programming problems

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this combination of uncertainty and randomness, we introduce the concept of an uncertain random variable and present a novel framework known as the linear-normal uncertain random variable. Our main focus in this work is the development of three distinct transformation techniques: the optimistic value criteria, pessimistic value criteria, and expected value criteria. These approaches allow us to convert a linear-normal uncertain random variable into a more manageable random variable. This transition facilitates the transformation from an uncertain random geometric programming problem to a stochastic geometric programming problem. Furthermore, we provide insights into an equivalent deterministic representation of the transformed geometric programming problem, enhancing the clarity and practicality of the optimization process. To demonstrate the effectiveness of our proposed approach, we present a numerical example.

math.OC↗

arXiv2023

Geometric Programming Problems with Triangular and Trapezoidal Two-fold Uncertainty Distributions

Geometric programming (GP) is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a GP problem are deterministic and accurate. However, in the real-world GP problem, the parameters are frequently inaccurate and ambiguous. This paper investigates the GP problem in an uncertain environment, with the coefficients as triangular and trapezoidal two-fold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated two-fold uncertainties to propose triangular and trapezoidal two-fold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal two-fold uncertain variables into single-fold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the GP problem with two-fold uncertainty into the GP problem with single-fold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced single-fold uncertain GP problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures.

math.OC↗