Primal separation algorithms

Primal-dual path-following algorithms for circular programming

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

Primal separation for 0/1 polytopes

The 0/1 primal separation problem is: Given an extreme point x̄ of a 0/1 polytope P and some point x , find an inequality which is tight at x̄, violated by x and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalen...

Margins, Kernels and Non-linear Smoothed Perceptrons

We focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view (giving a certificate of non-existence), with special focus on generalizations of two classical schemes the Perceptron (primal) and Von-Neumann (dual) algorithms....

Monotonicity of Primal and Dual Objective Values in Primal-dual Interior-point Algorithms

We study monotonicity of primal and dual objective values in the framework of primal-dual interior-point methods. The primal-dual aane-scaling algorithm is monotone in both objectives. We derive a condition under which a primal-dualinterior-point algorithm with a centering component is monotone. Then we propose primal-dual algorithms that are monotone in both primal and dual objective values an...