Abhishek Singh
I work on convergent numerical methods for multi-objective and vector optimization, building quasi-Newton, trust-region, and conjugate gradient algorithms and pushing them from the single-objective setting into the vector-valued one. My doctoral work developed inexact Newton and BFGS-type frameworks for generalized Nash equilibrium problems, with global and superlinear convergence results for multi-player games. That line of work now extends into unconstrained and constrained multi-objective optimization, aimed at methods that hold up both in theory and at scale.
- Managing Editor Applicable Nonlinear Analysis ↗
- Managing Editor Optimization Eruditorum ↗
Research interests
Academic appointments
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2024 –
2026Postdoctoral Researcher
National Center for Applied Mathematics, Chongqing Normal University, China- Designs and analyzes nonmonotone adaptive trust-region and quasi-Newton methods for unconstrained multi-objective optimization, proving global convergence under standard smoothness assumptions.
- Extends nonmonotone trust-region and conjugate gradient theory to vector-valued objectives; results submitted to Computational Optimization and Applications, Journal of Optimization Theory and Applications, and Journal of Global Optimization.
- Implements and benchmarks algorithms in MATLAB against state-of-the-art solvers on standard multi-objective test suites.
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2023Visiting Research Intern
National Sun Yat-sen University, Kaohsiung, Taiwan- Three-month visiting fellowship under Prof. Jen-Chih Yao researching vector optimization theory; the work was later formalized into a 2025 joint publication in Optimization.
Education
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2016 –
2023Ph.D., Mathematics (Optimization) — Indian Institute of Technology (BHU), Varanasi, India
Advisor: Dr. Debdas Ghosh · Thesis: "Optimization Methods to Solve Generalized Nash Equilibrium Problems" -
2011 –
2013M.Sc., Mathematical Sciences — VBS Purvanchal University, Jaunpur, India -
2008 –
2011B.Sc., Mathematics & Physics — VBS Purvanchal University, Jaunpur, India
Publications
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[1]
A trust-region algorithm with a \(T_k\)-based nonmonotone strategy for unconstrained multiobjective optimization
Journal of Nonlinear and Variational Analysis
(Accepted for publication)
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[2]
Improved nonmonotone quasi-Newton method for multiobjective optimization problems
Journal of Nonlinear and Convex Analysis, 27(1), 119–142 · 2026
Abstract
Surveys the components of quasi-Newton methods for multiobjective optimization — Hessian approximations, search directions, and step lengths — then proposes an improved nonmonotone BFGS-based scheme. Establishes well-posedness and global convergence under mild assumptions, with numerical results on standard test problems.
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[3]
A novel modified Liu–Storey nonlinear conjugate gradient method for solving vector optimization problems
Optimization, 1–30 · 2025 (Taylor & Francis)
Abstract
Addresses a gap in Gonçalves et al.'s Liu–Storey extension for vector optimization, where descent is not guaranteed even under exact line search. Proposes a modified Liu–Storey scheme with a standard Wolfe line search that restores descent and proves global convergence for nonconvex vector optimization problems, backed by numerical experiments.
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[4]
Inexact Newton method for solving generalized Nash equilibrium problems
Journal of Optimization Theory and Applications, 201(3), 1333–1363 · 2024 (Springer)
Abstract
Develops an inexact Newton method for player-convex and jointly convex generalized Nash equilibrium problems, reformulated via a complementarity function. Proves global convergence for both problem classes, with Q-quadratic convergence under strong BD-regularity and a suitable forcing sequence. Tested on an internet-switching game, outperforming an existing semi-smooth Newton method.
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[5]
Improved nonmonotone adaptive trust-region method to solve generalized Nash equilibrium problems
Journal of Nonlinear and Convex Analysis, 25(1), 11–29 · 2024
Abstract
Proposes an improved nonmonotone adaptive trust-region method for constrained optimization under loose error-bound conditions, applied to GNEPs where Newtonian methods often struggle with nonunique local solutions. Retains the local convergence properties of the nonmonotone trust-region method while adding global convergence, and outperforms it numerically.
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[6]
A globally convergent improved BFGS method for generalized Nash equilibrium problems
SeMA Journal, 81(2), 235–261 · 2024 (Springer)
Abstract
Solves a player-convex GNEP with an improved BFGS method using an Armijo–Goldstein line search rather than the costlier Wolfe-type search. Reworks the Hessian update so it keeps positive definiteness under Armijo-type search, proves global convergence, and tests the method on three standard GNEPs plus two internet-switching problems.
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[7]
Extended Karush–Kuhn–Tucker condition for constrained interval optimization problems and its application in support vector machines
Information Sciences, 504, 276–292 · 2019 (Elsevier)
Abstract
Derives extended Fritz John and Karush–Kuhn–Tucker optimality conditions for constrained interval optimization problems, built from the geometric fact that the cone of feasible directions and the set of descent directions cannot overlap at an optimum. Applies the result to binary classification with interval-valued data via support vector machines.
Conferences & workshops
- 2025ICOVA-2025 — International Conference on Optimization and Variational Analysis, Chongqing Normal University, China
- 2023Visiting research internship — National Sun Yat-sen University, Kaohsiung, Taiwan
- 2019ICCOPT 2019 — Weierstrass Institute (WIAS), Berlin, Germany
- 2019ICCOPT 2019 Summer School — WIAS, Berlin, Germany
- 2018ICMC 2018 — IIT (BHU), Varanasi, India
- 2017ICWAO 2017 — Aligarh Muslim University, Aligarh, India
Service & awards
Academic service
- Apr 2024 – presentManaging Editor, Applicable Nonlinear Analysis
- Managing Editor, Optimization Eruditorum
Awards & honors
- 2016CSIR-JRF, Mathematical Sciences — All India Rank 22
- 2015GATE, Mathematical Sciences — All India Rank 624