&ldquo;IIT Jodhpur is committed to impart quality education to facilitate the creation of qualified, competent and responsible human resources to meet the emerging technological challenges of the world. It is working towards creating an equitable learning platform that is positive, accessible and effective in the face of the modern societal and scientific advancements.

Flexibility in curriculum, in all its academic programs, encompassing elements of teaching, research, creativity, innovation and entrepreneurship is the most unique feature of IIT Jodhpur. The Department of Science and Technology (DST), under the National Mission on Cyber Physical Systems, has identified IIT Jodhpur as a Technology &amp; Innovation Hub in the area of Augmented Reality and Virtual Reality. The institute has also been nominated as the coordinator for the Jodhpur City and Knowledge Cluster by the Office of Principal Scientific Adviser, Government of India.

The sprawling 852-acre IIT Jodhpur campus is a majestic tribute to the deep-rooted diverse cultural heritage of the region. The campus is an architectural masterpiece, which is slated to become an international exemplar of sustainability with net-zero energy, and advanced water and waste management strategies.&rdquo;

IIT Jodhpur

In this article, the concept of the single-objective sequential quadratically constrained quadratic programming method is extended to the multiobjective case and a new line search technique is developed for nonlinear multiobjective optimization problems. The proposed method ensures global convergence as well as spreading of the Pareto front. A descent direction is obtained by solving a quadratically constrained quadratic programming subproblem. A nondifferentiable penalty function is used to restrict the constraint violations. Convergence of the descent sequence is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. In addition to this, a new technique is designed for selecting initial points to ensure the spreading of the Pareto front. The method is compared with existing methods using a set of test problems. © 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Department of Mathematics

World University root node

SIAM Journal on Optimization

A globally convergent sqcqp method for multiobjective optimization problems

The q-gradient is the generalization of the gradient based on the q-derivative. The q-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as q equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples. © 2020 the Author(s), licensee AIMS Press.

AIMS Mathematics

On Q-steepest descent method for unconstrained multiobjective 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. © 2020, Korean Society for Informatics and Computational Applied Mathematics.

Fulltext

Journal of Applied Mathematics and Computing

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

In this paper, we present a method of so-called q-Newton’s type descent direction for solving unconstrained multiobjective optimization problems. The algorithm presented in this paper is implemented by applying an independent parameter q (quantum) in an Armijo-like rule to compute the step length which guarantees that the value of the objective function decreases at every iteration. The search processes gradually shift from global in the beginning to local as the algorithm converges due to q-gradient. The algorithm is experimented on 41 benchmark/test functions which are unimodal and multi-modal with 1, 2, 3, 4, 5, 10 and 50 different dimensions. The performance of the proposed method is confirmed by comparing with three existing schemes. © 2020, Korean Society for Informatics and Computational Applied Mathematics.

On q-Newton’s method for unconstrained multiobjective optimization problems

In this article a line search algorithm is proposed for solving constrained multi-objective optimization problems. At every iteration of the proposed method, a subproblem is formulated using quadratic approximation of all functions. A feasible descent direction is obtained as a solution of this subproblem. This scheme takes care some ideas of the sequential quadratically constrained quadratic programming technique for single objective optimization problems. A non-differentiable penalty function is used to restrict constraint violations at every iterating point. Convergence of the scheme is justified under the Slater constraint qualification along with some reasonable assumptions. The proposed algorithm is verified and compared with existing methods with a set of test problems. It is observed that this algorithm provides better results in most of the test problems. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Engineering Optimization

A sequential quadratically constrained quadratic programming technique for a multi-objective optimization problem

Journal of Mathematical Analysis

A Variant of SQCQP Descent Scheme for Multi-objective Optimization Problem

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples. © 2014 Taylor & Francis.

Optimization

A modified Quasi-Newton method for vector optimization problem

We propose an implicit interval Newton algorithm for finding a root of a nonlinear equation. Our implicit process avoids the burden of selecting an initial point very close to the root as required by the classical Newton method. The conventional interval Newton method converges quadratically, while our modified algorithm converges cubically under some conditions and bi-quadratically under other conditions. These convergence results are proved using an image extension of a Taylor expansion. The algorithm is illustrated by numerical examples, and we provide a comparison between the existing interval Newton method and our proposed method.

Reliable Computing

New higher order root finding algorithm using interval analysis

This paper develops a methodology to generate a sequence of interval vectors (boxes), which converges to a very small box of negligible volume containing the minimum point a function of several variable. Each point of that box is an approximate solution. Interval extension of real valued function is used to propose the method. © 2012 Newswood Limited. All rights reserved.