Sturm, Jos F. 19712003
Overview
Works:  41 works in 101 publications in 1 language and 166 library holdings 

Roles:  Author, Honoree 
Classifications:  HB143, 330 
Publication Timeline
.
Most widely held works by
Jos F Sturm
Primaldual interior point approach to semidefinite programming by
Jos F Sturm(
Book
)
4 editions published in 1997 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1997 in English and held by 14 WorldCat member libraries worldwide
New complexity results for the IriImai method by
Jos F Sturm(
Book
)
4 editions published in 1993 in English and held by 10 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 10 WorldCat member libraries worldwide
A potential reduction method for harmonically convex programming by
Jos F Sturm(
Book
)
3 editions published in 1993 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 8 WorldCat member libraries worldwide
Superlinear convergence of a symmetric primaldual path following algorithm for semidefinite programming by
ZhiQuan Luo(
Book
)
4 editions published in 1996 in English and held by 7 WorldCat member libraries worldwide
This paper establishes the superlinear convergence of a symmetric primaldual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primaldual optimal solution and that the size of the central path neighborhood tends to zero. The interior point algorithm considered here closely resembles the MizunoToddYe predictorcorrector method for linear programming which is known to be quadratically convergent. It is shown that when the iterates are well centered, the duality gap is reduced superlinearly after each predictor step. Indeed, if each predictor step is succeeded by $r$ consecutive corrector steps then the predictor reduces the duality gap superlinearly with order $\frac{2}{1+2^{2r}}$. The proof relies on a careful analysis of the central path for semidefinite programming. It is shown that under the strict complementarity assumption, the primaldual central path converges to the analytic center of the primaldual optimal solution set, and the distance from any point on the central path to this analytic center is bounded by the duality gap
4 editions published in 1996 in English and held by 7 WorldCat member libraries worldwide
This paper establishes the superlinear convergence of a symmetric primaldual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primaldual optimal solution and that the size of the central path neighborhood tends to zero. The interior point algorithm considered here closely resembles the MizunoToddYe predictorcorrector method for linear programming which is known to be quadratically convergent. It is shown that when the iterates are well centered, the duality gap is reduced superlinearly after each predictor step. Indeed, if each predictor step is succeeded by $r$ consecutive corrector steps then the predictor reduces the duality gap superlinearly with order $\frac{2}{1+2^{2r}}$. The proof relies on a careful analysis of the central path for semidefinite programming. It is shown that under the strict complementarity assumption, the primaldual central path converges to the analytic center of the primaldual optimal solution set, and the distance from any point on the central path to this analytic center is bounded by the duality gap
An interior point subgradient method for linearly constrained nondifferentiable programming by
Hans Frenk(
Book
)
5 editions published in 1996 in English and held by 7 WorldCat member libraries worldwide
We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for minmax problems proposed by Sturm and Zhang \cite{SZ95}. In the new method, the search direction is obtained by projecting in a scaled space a subgradient of the objective function with a logarithmic barrier term. The stepsize choice is analogous to the stepsize choice in the usual subgradient method. Convergence of the method is established
5 editions published in 1996 in English and held by 7 WorldCat member libraries worldwide
We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for minmax problems proposed by Sturm and Zhang \cite{SZ95}. In the new method, the search direction is obtained by projecting in a scaled space a subgradient of the objective function with a logarithmic barrier term. The stepsize choice is analogous to the stepsize choice in the usual subgradient method. Convergence of the method is established
On sensitivity of central solutions in semidefinite programming by
Jos F Sturm(
Book
)
4 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Analytic central path, sensitivity analysis and parametric linear programming by
A. G Holder(
Book
)
5 editions published between 1997 and 1998 in English and held by 7 WorldCat member libraries worldwide
In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the righthand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is oneside differentiable with respect to the perturbation parameter. In that case we also show that the whole analytic central path shifts in a uniform fashion. When the objective vector is perturbed, we show that the last part of the analytic central path is tangent to a central path defined on the optimal face of the original problem
5 editions published between 1997 and 1998 in English and held by 7 WorldCat member libraries worldwide
In this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the righthand side vector of a standard linear program is perturbed, then the analytic center of the optimal face is oneside differentiable with respect to the perturbation parameter. In that case we also show that the whole analytic central path shifts in a uniform fashion. When the objective vector is perturbed, we show that the last part of the analytic central path is tangent to a central path defined on the optimal face of the original problem
A dual and interior point approach to solve convex minmax problems by
Jos F Sturm(
Book
)
4 editions published in 1995 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1995 in English and held by 7 WorldCat member libraries worldwide
Polynomial primaldual cone affine scaling for semidefinite programming by
Arjan B Berkelaar(
Book
)
5 editions published between 1996 and 1997 in English and held by 7 WorldCat member libraries worldwide
In this paper we generalize the primaldual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primaldual affine scaling algorithms for semidefinite programming, our algorithm enjoys the lowest computational complexity
5 editions published between 1996 and 1997 in English and held by 7 WorldCat member libraries worldwide
In this paper we generalize the primaldual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primaldual affine scaling algorithms for semidefinite programming, our algorithm enjoys the lowest computational complexity
Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution
exists by
Jos F Sturm(
Book
)
5 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
A new predictorcorrector interior point algorithm for solving monotone linear complementarity problems (LCP) is proposed, and it is shown to be superlinearly convergent with at least order 1.5, even if the LCP has no strictly complementary solution. Unlike Mizuno's recent algorithm (Mizuno, 1996), the fast local convergence is attained without any need for estimating the optimal partition. In the special case that a strictly complementary solution does exist, the order of convergence becomes quadratic. The proof relies on an investigation of the asymptotic behavior of first and second order derivatives that are associated with trajectories of weighted centers for LCP
5 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
A new predictorcorrector interior point algorithm for solving monotone linear complementarity problems (LCP) is proposed, and it is shown to be superlinearly convergent with at least order 1.5, even if the LCP has no strictly complementary solution. Unlike Mizuno's recent algorithm (Mizuno, 1996), the fast local convergence is attained without any need for estimating the optimal partition. In the special case that a strictly complementary solution does exist, the order of convergence becomes quadratic. The proof relies on an investigation of the asymptotic behavior of first and second order derivatives that are associated with trajectories of weighted centers for LCP
On a wide region of centers and primaldual interior point algorithms for linear programming by
Jos F Sturm(
Book
)
4 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
In the adaptive step primaldual interior point method for linear programming, polynomial algorithms are obtained by computing Newton directions towards targets on the central path, and restricting the iterates to a neighborhood of this central path. In this paper, the adaptive step methodology is extended, by considering targets in a certain central {\em region}, which contains the usual central path, and subsequently generating iterates in a neighborhood of this region. The size of the central region can vary from the central path to the whole feasible region by choosing a certain parameter. An \( {\cal O}( \sqrt{ n} L) \) iteration bound is obtained under very mild conditions on the choice of the target points. In particular, we leave plenty of room for experimentation with search directions. The practical performance of the new primaldual interior point method is measured on the Netlib test set for various sizes of the central region
4 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
In the adaptive step primaldual interior point method for linear programming, polynomial algorithms are obtained by computing Newton directions towards targets on the central path, and restricting the iterates to a neighborhood of this central path. In this paper, the adaptive step methodology is extended, by considering targets in a certain central {\em region}, which contains the usual central path, and subsequently generating iterates in a neighborhood of this region. The size of the central region can vary from the central path to the whole feasible region by choosing a certain parameter. An \( {\cal O}( \sqrt{ n} L) \) iteration bound is obtained under very mild conditions on the choice of the target points. In particular, we leave plenty of room for experimentation with search directions. The practical performance of the new primaldual interior point method is measured on the Netlib test set for various sizes of the central region
On weighted centers for semidefinitive programming by
Jos F Sturm(
Book
)
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weighted centers. Relations with other primaldual maps are discussed
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weighted centers. Relations with other primaldual maps are discussed
An interior point method, based on rankone updates, for linear programming by
Jos F Sturm(
Book
)
4 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
We propose a polynomial time primaldual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rankone updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the number of operations required is ${\cal O}(mn)$ per main iteration and the overall computational complexity is ${\cal O}(mn^{2.5}L)$
4 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
We propose a polynomial time primaldual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rankone updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the number of operations required is ${\cal O}(mn)$ per main iteration and the overall computational complexity is ${\cal O}(mn^{2.5}L)$
Symmetric primaldual path following algorithms for semidefinite programming by
Jos F Sturm(
Book
)
5 editions published between 1995 and 1996 in English and held by 6 WorldCat member libraries worldwide
In this paper a symmetric primaldual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primaldual transformation is a well known fact. Based on this symmetric primaldual transformation we derive Newton search directions for primaldual pathfollowing algorithms for semidefinite programming. In particular, we generalize: (1) the short step path following algorithm, (2) the predictorcorrector algorithm and (3) the largest step algorithm to semidefinite programming. It is shown that these algorithms require at most ${\cal O}(\sqrt{n}\mid \log \epsilon \mid ) $ main iterations for computing an $\epsilon $optimal solution
5 editions published between 1995 and 1996 in English and held by 6 WorldCat member libraries worldwide
In this paper a symmetric primaldual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primaldual transformation is a well known fact. Based on this symmetric primaldual transformation we derive Newton search directions for primaldual pathfollowing algorithms for semidefinite programming. In particular, we generalize: (1) the short step path following algorithm, (2) the predictorcorrector algorithm and (3) the largest step algorithm to semidefinite programming. It is shown that these algorithms require at most ${\cal O}(\sqrt{n}\mid \log \epsilon \mid ) $ main iterations for computing an $\epsilon $optimal solution
Duality and selfduality for conic convex programming by
ZhiQuan Luo(
Book
)
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular, we introduce the notions of weak/strong feasibility or infeasibility for a general primaldual pair of conic convex programs, and then establish various relations between these notions and the duality properties of the problem. In the second half of the paper, we propose a selfdual embedding with the following properties: Any weakly centered sequence converging to a complementary pair either induces a sequence converging to a certificate of strong infeasibility, or induces a sequence of primaldual pairs for which the amount of constraint violation converges to zero, and the corresponding objective values are in the limit not worse than the optimal objective value(s). In case of strong duality, these objective values in fact converge to the optimal value of the original problem. When the problem is neither strongly infeasible nor endowed with a complementary pair, we completely specify the asymptotic behavior of an indicator in relation to the status of the original problem, namely whether the problem (1) is weakly infeasible, (2) is feasible but with a positive duality gap, (3) has no duality gap nor complementary solution pair
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular, we introduce the notions of weak/strong feasibility or infeasibility for a general primaldual pair of conic convex programs, and then establish various relations between these notions and the duality properties of the problem. In the second half of the paper, we propose a selfdual embedding with the following properties: Any weakly centered sequence converging to a complementary pair either induces a sequence converging to a certificate of strong infeasibility, or induces a sequence of primaldual pairs for which the amount of constraint violation converges to zero, and the corresponding objective values are in the limit not worse than the optimal objective value(s). In case of strong duality, these objective values in fact converge to the optimal value of the original problem. When the problem is neither strongly infeasible nor endowed with a complementary pair, we completely specify the asymptotic behavior of an indicator in relation to the status of the original problem, namely whether the problem (1) is weakly infeasible, (2) is feasible but with a positive duality gap, (3) has no duality gap nor complementary solution pair
On the long step pathfollowing method for semidefinite programming by
Jos F Sturm(
Book
)
4 editions published in 1996 in English and held by 4 WorldCat member libraries worldwide
It has been shown in various recent research reports that the analysis of short step primaldual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long step pathfollowing algorithms for semidefinite programming appeared to be less straightforward. For such an algorithm, Monteiro obtained an O(n^1.5 log(1/ epsilon)) iteration bound for obtaining an epsilonoptimal solution, where n is the order of the semidefinite decision variable. In this paper, we propose to use a different search direction, viz. the socalled Vspace direction. It is shown that this modification reduces the iteration complexity to O(n log(1/ epsilon)) . Independently, Monteiro and Y.Zhang obtained a similar result using NesterovTodd directions
4 editions published in 1996 in English and held by 4 WorldCat member libraries worldwide
It has been shown in various recent research reports that the analysis of short step primaldual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long step pathfollowing algorithms for semidefinite programming appeared to be less straightforward. For such an algorithm, Monteiro obtained an O(n^1.5 log(1/ epsilon)) iteration bound for obtaining an epsilonoptimal solution, where n is the order of the semidefinite decision variable. In this paper, we propose to use a different search direction, viz. the socalled Vspace direction. It is shown that this modification reduces the iteration complexity to O(n log(1/ epsilon)) . Independently, Monteiro and Y.Zhang obtained a similar result using NesterovTodd directions
Robust one period option modelling by
Frank Lutgens(
Book
)
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
On cones of nonnegative quadratic functions by
Jos F Sturm(
Book
)
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
Avoiding numerical cancellation in the interior point method for solving semidefinite programs by
Jos F Sturm(
Book
)
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
Implementation of interior point methods for mixed semidefinite and second order cone optimization problems by
Jos F Sturm(
Book
)
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Zhang, Shuzhong
 Luo, ZhiQuan Author
 Tinbergen Institute
 Center for Economic Research
 Berkelaar, Arjan B. (Arjan Bastiaan) 1972 Author
 Frenk, J. B. G. Author
 Holder, A. G. Author
 Lutgens, Frank (Frank Johannes Willem) 1977 Author
 Luo, ZhiQuan Author
 Luo, Z.Q Author
Associated Subjects
Alternative Names
Sturm, J. F.
Sturm, J. F. 19712003
Sturm, J. F. (Jos F.)
Sturm, Jos 19712003
Sturm, Jos Fredrik 19712003
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