Pattern separation by convex programming

Pattern separation via ellipsoids and conic programming

Nonparametric Estimation by Convex Programming

The problem we concentrate on is as follows: given (1) a convex compact set X in R, an affine mapping x 7→ A(x), a parametric family {pμ(·)} of probability densities and (2) N i.i.d. observations of the random variable ω, distributed with the density pA(x)(·) for some (unknown) x ∈X, estimate the value gx of a given linear form at x. For several families {pμ(·)} with no additional assumptions o...

Pattern classification by convex analysis

A useful discriminant vector for pattern classification is one that maximizes the minimum separation of discriminant function values for two pattern classes. This optimality criterion can prove valuable in many situations because it emphasizes the class elements that are most difficult to classify. A method for computing this discriminant vector by quadratic programming is derived. The resultin...

Convex approximations in stochastic programming by semidefinite programming

The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in L1, L∞ and L2 norm. Extensive numerical experiments to ...

Reconstructing Convex Matrices by Integer Programming Approaches

We consider the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of adjacent ones. We reformulate the problem by using integer programming and we develop approximate solutions based on linearization and convexification techniques.