An approach, based on conic splines, is proposed here for capturing image outlines of generic shapes. It has various phases including extracting outlines of images, mining feature points from the detected outlines, and curve fitting. The idea of particle swarm optimization has been incorporated to optimize the shape parameters in the description of the conic spline. The method ultimately produc...

Abstract. We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when U is given as the intersection of ellipsoids or as an n-dimensional box. For these cases we...

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique,...

Space tensors appear in physics and mechanics, and they are real physical entities. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint o...

In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of “no duality gap” and existence of optimal solutions are rel...

Format (5.1.1) covers all uncertain optimization problems considered so far; moreover, in these latter problems the objective f and the right hand side F of the constraints always were bi-affine in x, ζ, (that is, affine in x when ζ is fixed, and affine in ζ, x being fixed), and K was a “simple” convex cone (a direct product of nonnegative rays/Lorentz cones/Semidefinite cones, depending on whe...

We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then use a nonsmooth Newton method to find a solution; we apply the basic idea to the Splitting Cone Solver (SCS), a state-of-the-art method for solving generic c...

We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arb...

We analyse the scaling matrix, search direction, and neighbourhood used in MOSEK's algorithm for nonsymmetric conic optimization [J. Dahl E.D. Andersen, A primal-dual interior-point f...

In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show t...