Two Optimal Value Functions in Parametric Conic Linear Programming

Linear Conic Programming

A little story in the development of semidefinite programming. One day in 1990, I visited the Computer Science Department of the University of Min-nesota and met a young graduate student, Farid Alizadeh. He, working then on combinatorial optimization, introduced me " semidefinite optimization " or linear programming over the positive definite matrix cone. We had a very extensive discussion that...

Optimal value range in interval linear programming

Subgradients of value functions in parametric dynamic programming

We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are ob...

Subgradients of value functions in parametric dynamic programming q

We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are ob...

Linear discrimination using second order conic programming

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to linear programming problem with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc). The ...