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Thesis Defence: Computing the conjugate of nonconvex bivariate piecewise linear-quadratic functions
June 18 at 9:00 am - 1:00 pm
Tanmaya Karmarkar, supervised by Dr. Yves Lucet, will defend their thesis titled “Computing the conjugate of nonconvex bivariate piecewise linear-quadratic functions” in partial fulfillment of the requirements for the degree of Master of Science in Computer Science.
An abstract for Tanmaya Karmarkar’s thesis is included below.
Defences are open to all members of the campus community as well as the general public. This defence will be offered in hybrid format. Registration is not required to attend in person defences; however, please email yves.lucet@ubc.ca to receive the Zoom link for this defence.
ABSTRACT
Computing the minima of a convex function is much easier than computing the same for a nonconvex function. Since every nonconvex function shares the same minima as its convex envelope, we compute the conjugate of a bivariate piecewise linear-quadratic (PLQ) function as a first step toward the computation of the convex envelope.
Our algorithm starts with computing the convex envelope of each piece obtaining a rational function defined over a polyhedral subdivision. Then we compute the conjugate of each of those pieces and obtain a fractional form defined over a parabolic subdivision. The last step is to compute the maximum of all those functions to obtain the conjugate of the original piecewise linear-quadratic function as a piecewise function defined on a parabolic subdivision.
Our implementation in MATLAB uses symbolic computation and rational numbers to avoid any floating-point errors.
