arXiv subjects

Geetanjali Panda

Publications and source records attributed to Geetanjali Panda.

5 recordsLinked to original sources

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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arXiv2019

On Critical Point for Functions with Bounded Parameters

Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a critical point. First, sufficient condition for the existence of descent direction is studied for this function and then a set of descent directions at a point is determined using linear expansion. Using these results a descent sequence of intervals is generated and critical point is characterized. This theoretical development is justified with numerical example.

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arXiv2019

Expansion of Generalized Hukuhara Differentiable Interval Valued Function

In this article, the concept of $μ-$ monotonic property of interval-valued function in higher dimension is introduced. Expansion of interval-valued function in higher dimension is developed using this property. Generalized Hukuhara differentiability is used to derive the theoretical results. Several examples are provided to justify the theoretical developments.

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arXiv2018

A Two-Phase Quasi-Newton Method for Optimization Problem

In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear rate of the scheme is also proved in the vicinity of the solution. The advantages of the proposed scheme over the traditional scheme are justified with numerical table and graphical illustrations.

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arXiv2017

q-Line Search Scheme for Optimization Problem

In this paper new descent line search iterative schemes for unconstrained as well as constrained optimization problems are developed using q-derivative. At every iteration of the scheme, a positive definite matrix is provided which is neither exact Hessian of the objective function as in Newton scheme nor the positive definite matrix as generated in quasi-Newton scheme. Second order differentiablity property is not required in this process. Component of this matrix are constructed using q-derivative of the function. It is proved that the schemes preserve the property of Newton-like schemes in a local neighborhood of a minimum point which leads to the super linear rate of convergence. Numerical illustration of the scheme is also provided.

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