Department of Computer Science & Engineering

&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

School of Artificial Intelligence and Data Science (AIDE)

Evolutionary algorithms (EAs) are increasingly being applied to solve real-parameter optimization problems due to their flexibility in handling complexities such as non-convexity, non-differentiability, multi-modality and noise in problems. However, an EA's solution is never guaranteed to be optimal in generic problems, even for smooth problems, and importantly EAs still lack a theoretically motivated termination criterion for stopping an EA run only when a near-optimal point is found. We address both these issues in this paper by integrating the Karush-Kuhn-Tucker (KKT) optimality conditions that involve first-order derivatives of objective and constraint functions with an EA. For this purpose, we define a KKT-proximity measure by relaxing the complimentary slackness condition associated with the KKT conditions. Results on a number of standard constrained test problems indicate that in spite of not using any gradient information and any theoretical optimality conditions, an EA's selection, recombination and mutation operation lead the search process to a point close to the KKT point. This suggests that the proposed KKT-proximity measure can be used a termination criterion in an EA simulation. Copyright 2010 ACM.

World University root node

Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10

Investigating EA solutions for approximate KKT conditions in smooth problems

We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The algorithm developed estimates the direction of steepest-descent rapidly and using Armijo's condition proceeds towards the solution. Owing to the highly parallel nature of the algorithm, it is highly suitable for large minimax problems. Algorithm is implemented on Nvidia Tesla C1060 graphics card using CUDA and numerical comparisons with RGA & CFSQP are presented. © 2010 Springer-Verlag.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A parallel algorithm for solving large convex minimax problems

In this note we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the approximate multiplier rule. © 2009 Springer and Mathematical Programming Society.

Mathematical Programming

A note on an approximate lagrange multiplier rule

This paper presents some results concerning the existence of the Lagrange multipliers for vector optimization problems in the case where the ordering cone in the codomain has an empty interior. The main tool for deriving our assertions is a scalarization by means of a functional introduced by Hiriart-Urruty (Math. Oper. Res. 4:79-97, 1979) (the so-called oriented distance function). Moreover, we explain some applications of our results to a vector equilibrium problem, to a vector control-approximation problem and to an unconstrainted vector fractional programming problem. © Springer Science+Business Media, LLC 2009.

Journal of Optimization Theory and Applications

Lagrange multipliers for ε-pareto solutions in vector optimization with nonsolid cones in banach spaces

A significant controversy regarding the climate history of the Earth and its relationship to the development of complex life forms concerns the rise of oxygen in the early Earth's atmosphere. Geological records show that this rise occurred about 2.4 Gyr ago, when the atmospheric oxygen increased from less than 10-5 present atmospheric level (PAL) to more than 0.01 PAL and possibly above 0.1 PAL. However, there is a debate whether this rise happened relatively smoothly or with well-pronounced ups and downs (the Yoyo model). In our study, we explore a simplified atmospheric chemical system consisting of oxygen, methane, and carbon that is driven by the sudden decline of the net input of reductants to the surface as previously considered by Goldblatt et al. Based on the transition stability analysis for the system equations, constituting a set of non-autonomous and non-linear differential equations, as well as the inspection of the Lyapunov exponents, it is found that the equations do not exhibit chaotic behavior. In addition, the rise of oxygen occurs relative smoothly, possibly with minor bumps (within a factor of 1.2), but without major jumps. This result clearly argues against the Yoyo model in agreement with recent geological findings. © 2009 The American Astronomical Society. All rights reserved.

Astrophysical Journal

The great oxidation of earth's atmosphere: Contesting the Yoyo model via transition stability analysis

A general method is developed to derive a Lagrangian and Hamiltonian for a nonlinear system with a quadratic first-order time derivative term and coefficients varying in the space coordinates. The method is based on variable transformations that allow removing the quadratic term and writing the equation of motion in standard form. Based on this form, an auxiliary Lagrangian for the transformed variables is derived and used to obtain the Lagrangian and Hamiltonian for the original variables. An interesting result is that the obtained Lagrangian and Hamiltonian can be non-local quantities, which do not diverge as the system evolves in time. Applications of the method to several systems with different coefficients shows that the method may become an important tool in studying nonlinear dynamical systems with a quadratic velocity term. © 2007 Elsevier Ltd. All rights reserved.

Chaos, Solitons and Fractals

Method to derive Lagrangian and Hamiltonian for a nonlinear dynamical system with variable coefficients

This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.

Journal of Convex Analysis

Monotonic analysis over cones: III

The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well. © 2008 Elsevier Inc. All rights reserved.

Fulltext

Journal of Mathematical Analysis and Applications

Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension

In this paper our focus is to study necessary optimality conditions for nonsmooth vector optimization problems in Banach spaces. Since in most infinite dimensional spaces the natural ordering cone has an empty interior it becomes quiet difficult to study vector optimization problems. This is due to the fact that we do not have powerful scalarization techniques in such a situation. In this paper we show how we can overcome such difficulties by using the notion of dilating cones. © 2008 Yokohama Publishers.

Pacific Journal of Optimization

Lagrange multipliers for pareto minima in general banach spaces

It is well known that the generalized Nash equilibrium problem, a model for multi-leader-follower games, can be reformulated as a quasivariational inequality. We show that, in fact, a reformulation in terms of a variational inequality can be obtained in the general setting of quasiconvex nondifferentiable decision functions. An existence result is deduced. © 2008 Elsevier B.V. All rights reserved.