This paper presents a new formulation of multi-instance learning as maximum margin problem, which is an extension of the standard C-support vector classification. For linear classification, this extension leads to, instead of a mixed integer quadratic programming, a continuous optimization problem, where the objective function is convex quadratic and the constraints are either linear or bilinea...

The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. The standard search directions for interior-point methods applied to self-scaled conic programming problems are the so-called Nesterov-Todd directions. In this article we show that these direct...

We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondifferentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maximization, quadratic programming, network flows), because they are simple, can exploit sparsity and in certain cases are highly parallelizable. We establish their global convergence ...

An iteration of the sequential quadratically constrained quadratic programming method (SQCQP) consists of minimizing a quadratic approximation of the objective function subject to quadratic approximation of the constraints, followed by a linesearch in the obtained direction. Methods of this class are receiving attention due to the development of efficient interior point techniques for solving s...

In this paper we analyze the parallel approximability of two special classes of Quadratic Programming. First, we consider Convex Quadratic Programming. We show that the problem of Approximating Convex Quadratic Programming is P-complete. We also consider two approximation problems related to it, Solution Approximation and Value Approximation and show both of these cannot be solved in NC, unless...

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model...

We investigate the problem (P̃ ) of minimizing f̃(x) := f(x) + p(x) subject to x ∈ D, where f(x) := x Ax + b x, A is a symmetric positive definite n-by-n matrix, b ∈ R, D ⊂ R is convex, and p : R → R satisfies supx∈D |p(x)| ≤ s for some given s < +∞. p is called perturbation, but it may describe some errors caused by modeling, measurement, approximation and calculation. We prove that the strict c...

This thesis presents a study of five different Lagrangian heuristics applied to the strictly convex quadratic minimum cost network flow problem. Tests are conducted on randomly generated transportation networks with different degrees of sparsity and nonlinearity according to a system devised by Ohuchi and Kaji [18]. The different heuristics performance in time and quality are compared. The unco...