# Convex

Thursday, May 21, 2015 - 9:00am - 9:50am

Fitting a low-rank matrix to data is an inherently non-convex problem; correspondingly, an increasingly common instinct has been to relax the rank constraint to a convex one, with the resulting estimator shown to be consistent under further statistical/structural assumptions.

However, this approach is rarely taken in practice, because it wastefully increases both the computational complexity and the search space of solutions.

However, this approach is rarely taken in practice, because it wastefully increases both the computational complexity and the search space of solutions.

Tuesday, February 24, 2015 - 10:15am - 11:05am

Kazuo Murota (University of Tokyo)

A discrete analogue of the theory of DC programming is constructed

on the basis of discrete convex analysis.

Since there are two classes of discrete convex functions (M-convex

functions and L-convex functions),

there are four types of discrete DC functions

(an M-convex function minus an M-convex function, an M-convex function minus an L-convex function, and so on) and four types of DC programs.

The discrete Toland-Singer duality establishes the relation among the four types of discrete DC programs.

on the basis of discrete convex analysis.

Since there are two classes of discrete convex functions (M-convex

functions and L-convex functions),

there are four types of discrete DC functions

(an M-convex function minus an M-convex function, an M-convex function minus an L-convex function, and so on) and four types of DC programs.

The discrete Toland-Singer duality establishes the relation among the four types of discrete DC programs.

Wednesday, May 30, 2012 - 4:30pm - 5:00pm

Maria Alfonseca-Cubero (North Dakota State University)

There are many open problems related to the reconstruction of an origin-symmetric convex body K in Rn from its lower dimensional information (areas of sections or projections, perimeters of sections or projections, length of cords, etc.)

In this talk we will survey known results on the determination of a convex body from its central sections, parallel sections, or maximal sections. Some of these problems have been long-time open, and a few very recent results will be presented.

In this talk we will survey known results on the determination of a convex body from its central sections, parallel sections, or maximal sections. Some of these problems have been long-time open, and a few very recent results will be presented.