FEASIBLE INTERIOR POINT METHOD FOR LINEAR COMPLEMENTARITY PROBLEM

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dc.contributor.authorCHALEKH RANDA
dc.date.accessioned2025-01-15T08:36:01Z
dc.date.available2025-01-15T08:36:01Z
dc.date.issued2024
dc.description.abstractThe purpose of this study is to solve the linear complementarity problem (LCP). To this end, we divided this work into two parts. In the first half, we provide an interior-point algorithm based on two novel parametric kernel functions. Proving that, under suitable assumptions, we guarantee the existence and uniqueness of the solution to the LCP. Afterwards, we show that a certain choice of the barrier degrees of our functions coincide with the best-known iteration bound for large-update methods. Finally, we offer some numerical results that prove the utility of the proposed algorithm. In the second part, we employ a smoothing-type algorithm and assuming a reasonable assumption, we can describe the LCP as an NP-hard absolute value equation (AVE). So we must rewrite AVE as a set of smooth equations and introduce two smoothing functions. Then, we show that the method is welldefined when the singular values of the matrix related to AVE exceed one and that it is convergent under the same assumption. We also demonstrate the numerical efficacy of this algorithm using these two functions.
dc.identifier.urihttps://dspace.univ-batna2.dz/handle/123456789/1834
dc.language.isoen
dc.titleFEASIBLE INTERIOR POINT METHOD FOR LINEAR COMPLEMENTARITY PROBLEM
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