Results 1  10
of
11
R.: Robust nearseparable nonnegative matrix factorization using linear optimization
 Journal of Machine Learning Research
, 2014
"... ar ..."
(Show Context)
Proximity queries between convex objects: An interior point approach for implicit surfaces
 IN 2006 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2006
"... This paper presents an interior point approach to exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make contact, such as in dynamic simulatio ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
This paper presents an interior point approach to exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make contact, such as in dynamic simulations and in contact point prediction for dextrous manipulation. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem; this optimization formulation has been previously described for polyhedral objects. We demonstrate that for general convex objects represented as implicit surfaces, interior point approaches are sufficiently fast, and owing to their global convergence properties, are the only provably good choice for solving proximity query problems for some object classes. We use a primaldual interior point algorithm that solves the KKT conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n 1.5), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is O(n 1.5).
On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming
"... presented to the University of Waterloo ..."
(Show Context)
A pCone Sequential Relaxation Procedure for 01 Integer Programs
, 2009
"... Several authors have introduced sequential relaxation techniques — based on linear and/or semidefinite programming — to generate the convex hull of 01 integer points in a polytope in at most n steps. In this paper, we introduce a sequential relaxation technique, which is based on porder cone progr ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Several authors have introduced sequential relaxation techniques — based on linear and/or semidefinite programming — to generate the convex hull of 01 integer points in a polytope in at most n steps. In this paper, we introduce a sequential relaxation technique, which is based on porder cone programming (1 ≤ p ≤ ∞). We prove that our technique generates the convex hull of 01 solutions asymptotically. In addition, we show that our method generalizes and subsumes several existing methods. For example, when p = ∞, our method corresponds to the wellknown procedure of Lovász and Schrijver based on linear programming. Although the porder cone programs in general sacrifice some strength compared to the analogous linear and semidefinite programs, we show that for p = 2 they enjoy a better theoretical iteration complexity. Computational considerations of our technique are discussed.
Epigraphical cones I
 JOURNAL OF CONVEX ANALYSIS, 2011, IN PRESS
"... Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1 is the epigraph of a nonnegative sublinear function f: Rn → R. This work explores the link between the geometric properties of K and the analytic properties of f. ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1 is the epigraph of a nonnegative sublinear function f: Rn → R. This work explores the link between the geometric properties of K and the analytic properties of f.
Characterizations of solution sets of coneconstrained convex programming problems
, 2015
"... Abstract In this paper, we consider a type of coneconstrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an opti ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract In this paper, we consider a type of coneconstrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies the corresponding results in Jeyakumar et al. (J Optim Theory Appl 123(1), 2004). In particular, when the cone reduces to three specific cones, that is, the porder cone, L p cone and circular cone, we show that the obtained results can be achieved by easier ways by exploiting the special structure of those three cones.
An interiorpoint method for the singlefacility location problem with mixed norms using a conic formulation
"... Abstract We consider the singlefacility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R n , where each distance can be measured according to a different pnorm. We show how this problem can be expressed into a st ..."
Abstract
 Add to MetaCart
Abstract We consider the singlefacility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R n , where each distance can be measured according to a different pnorm. We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving threedimensional cones. Using the availability of a selfconcordant barrier for these cones, we present a polynomialtime algorithm (a longstep pathfollowing interiorpoint scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.
On pnorm linear discrimination
"... We consider a pnorm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with porder cone constraints. The proposed approach for handling linear programming problems with porder cone constraints is based on reformulat ..."
Abstract
 Add to MetaCart
(Show Context)
We consider a pnorm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with porder cone constraints. The proposed approach for handling linear programming problems with porder cone constraints is based on reformulation of porder cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an “economical ” representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.
On polyhedral approximations in porder cone programming
"... This paper discusses the use of polyhedral approximations in solving of porder cone programming (pOCP) problems, or linear problems with porder cone constraints, and their mixed integer extensions. In particular, it is shown that the cuttingplane technique proposed in Krokhmal and Soberanis (2010 ..."
Abstract
 Add to MetaCart
This paper discusses the use of polyhedral approximations in solving of porder cone programming (pOCP) problems, or linear problems with porder cone constraints, and their mixed integer extensions. In particular, it is shown that the cuttingplane technique proposed in Krokhmal and Soberanis (2010) for a special type of polyhedral approximations of pOCP problems, which allows for generation of cuts in a constant time not dependent on the accuracy of approximation, is applicable to a larger family of polyhedral approximations, and can further be extended to form an essentially exact solution method for pOCP problems. Moreover, it is demonstrated that an analogous constanttime cut generating algorithm exists for (recursively constructed) lifted polyhedral approximations of secondorder cones due to BenTal and Nemirovski (2001). It is also shown that the developed polyhedral approximations and the corresponding cutting plane solution methods can be efficiently used for obtaining exact solutions of mixed integer pOCP problems.