Results 1  10
of
30
Duality Results For Conic Convex Programming
, 1997
"... This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone infinite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are give ..."
Abstract

Cited by 26 (11 self)
 Add to MetaCart
This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone infinite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include GordonStiemke type theorems, Farkas type theorems, perfect duality, Slater condition, regularization, Ramana's duality, and approximate dualities. The dual representations of various convex sets, convex cones and conic convex programs are also discussed.
Copositive Relaxation for General Quadratic Programming
 OPTIM. METHODS SOFTW
, 1998
"... We consider general, typically nonconvex, Quadratic Programming Problems. The Semidefinite relaxation proposed by Shor provides bounds on the optimal solution, but it does not always provide sufficiently strong bounds if linear constraints are also involved. To get rid of the linear sideconstraint ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
We consider general, typically nonconvex, Quadratic Programming Problems. The Semidefinite relaxation proposed by Shor provides bounds on the optimal solution, but it does not always provide sufficiently strong bounds if linear constraints are also involved. To get rid of the linear sideconstraints, another, stronger convex relaxation is derived. This relaxation uses copositive matrices. Special cases are discussed for which both relaxations are equal. At the end of the paper, the complexity and solvability of the relaxations are discussed.
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
(Show Context)
Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.
Infeasible Start Semidefinite Programming Algorithms Via SelfDual Embeddings
, 1997
"... The development of algorithms for semidefinite programming is an active research area, based on extensions of interior point methods for linear programming. As semidefinite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
The development of algorithms for semidefinite programming is an active research area, based on extensions of interior point methods for linear programming. As semidefinite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of infeasibility, nonzero optimal duality gaps, etc. Infeasible start algorithms have been proposed which yield different kinds of information about the solution. In this paper a comprehensive treatment of a specific initialization strategy is presented, namely selfdual embedding, where the original primal and dual problems are embedded in a larger problem with a known interior feasible starting point. A framework for infeasible start algorithms with the best obtainable complexity bound is thus presented. The information that can be obtained in case of infeasibility, unboundedness, etc., is stated clearly. Important unresolved issues are discussed.
Global Optimization Problems in Computer Vision
 In C.A. Floudas and P.M. Pardalos, editors, State of the Art in Global Optimization
, 1995
"... In the field of computer vision, computer scientists extract knowledge from an image by manipulating it through image transforms. In the mathematical language of image algebra an image transformation often CO1Tesponds to an imagetemplate product. When performing this operation on a computer, saving ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
In the field of computer vision, computer scientists extract knowledge from an image by manipulating it through image transforms. In the mathematical language of image algebra an image transformation often CO1Tesponds to an imagetemplate product. When performing this operation on a computer, savings in time and memory as well as a better fit to the specific computer architecture can often be achieved by using the technique of template decomposition. In this paper we use global optimization techniques to solve a general problem of morphological template decomposition.
Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms
, 2001
"... A form p on R n (homogeneous nvariate polynomial) is called positive semidenite (p.s.d.) if it is nonnegative on R n . In other words, the zero vector is a global minimizer of p in this case. The famous 17th conjecture of Hilbert [9] (later proven by Artin [1]) is that a form p is p.s.d. if and ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
A form p on R n (homogeneous nvariate polynomial) is called positive semidenite (p.s.d.) if it is nonnegative on R n . In other words, the zero vector is a global minimizer of p in this case. The famous 17th conjecture of Hilbert [9] (later proven by Artin [1]) is that a form p is p.s.d. if and only if it can be decomposed a sum of squares of rational functions. In this paper we give an algorithm to compute such a decomposition for ternary forms (n = 3). This algorithm involves the solution of a series of systems of linear matrix inequalities (LMI's). In particular, for a given p.s.d. ternary form p of degree 2m, we show that the abovementioned decomposition can be computed by solving at most m=4 systems of LMI's of dimensions polynomial in m. The underlying methodology is largely inspired by the original proof of Hilbert, who had been able to prove his conjecture for the case of ternary forms. 1
ENHANCING COLLABORATIVE PEERTOPEER SYSTEMS USING RESOURCE AGGREGATION AND CACHING: A MULTIATTRIBUTE RESOURCE AND QUERY AWARE APPROACH
"... Resourcerich computing devices, decreasing communication costs, and Web 2.0 technologies are fundamentally changing the way distributed applications communicate and collaborate. With these changes, we envision PeertoPeer (P2P) systems that will allow for the integration and collaboration of peers ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Resourcerich computing devices, decreasing communication costs, and Web 2.0 technologies are fundamentally changing the way distributed applications communicate and collaborate. With these changes, we envision PeertoPeer (P2P) systems that will allow for the integration and collaboration of peers with diverse capabilities to a virtual community thereby empowering it to engage in greater tasks beyond what can be accomplished by individual peers, yet are beneficial to all the peers. Collaborations involving applicationspecific resources and dynamic quality of service goals will stress current P2P architectures that are designed for besteffort environments with pairwise interactions among nodes with similar resources. These systems will share a variety of resources such as processor cycles, storage capacity, network bandwidth, sensors/actuators, services, middleware, scientific algorithms, and data. However, very little is known about the specific characteristics of realworld resources and queries as well as their impact on resource aggregation in these collaborative P2P systems. We developed resource discovery, caching, and distributed data fusion solutions that are more suitable for collaborative P2P systems while characterizing realworld resource, query, and user behavior. The contributions of this research are: (1) a detailed analysis of realworld resource, query, and user characteristics and their impact on resource discovery solutions, (2) a tool to generate large synthetic traces of multiattribute resources and range queries,
An optimal onoff controller with switching costs using nonlinear binary programming
 Proc. American Control Conference, St. Louis, MO
, 2009
"... Abstract — Autonomous systems based on MEMS devices may often be provided with very limited computational and power capacity, if control circuitry and power sources are to be miniaturized along with the electromechanical components. OnOff control can serve as an efficient methods of regulating moti ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract — Autonomous systems based on MEMS devices may often be provided with very limited computational and power capacity, if control circuitry and power sources are to be miniaturized along with the electromechanical components. OnOff control can serve as an efficient methods of regulating motion of MEMS structures when power is extremely limited by allowing control to be performed using simple driving circuits and few transitions between ‘on’ and ‘off’states. In particular, this is highly desirable for microrobotics applications based on piezoelectric actuation. In this paper a binary programming method is used to optimize a cost function that consists of the number of switching transitions and ontime for a lineardiscrete system, as the system is steered to a desired final state. This can be used to minimize power consumption in piezoelectric actuators as they move a microrobotic leg joint to a desired position. A set of test cases is examined to explore behavior of the optimization procedure. I.
Optimal Bit and Power Loading for AmplifyandForward Cooperative OFDM Systems
"... Abstract—In this paper, we investigate bit and power allocation strategies for an orthogonal frequency division multiplexing (OFDM) cooperative network over frequencyselective fading channels. We assume amplifyandforward relaying and consider the bit error rate (BER) performance as our performanc ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract—In this paper, we investigate bit and power allocation strategies for an orthogonal frequency division multiplexing (OFDM) cooperative network over frequencyselective fading channels. We assume amplifyandforward relaying and consider the bit error rate (BER) performance as our performance measure. Aiming to optimize the BER under total power constraint and for a given average data rate, we propose three adaptive algorithms; optimal power loading (OPL), optimal bit loading (OBL), and optimal joint bit and power loading (OBPL). Our Monte Carlo simulation results demonstrate performance gains through adaptive bit and power loading over conventional nonadaptive systems as well as currently available adaptive cooperative scheme in the literature. The impact of practical issues on the performance of proposed adaptive schemes such as imperfect channel estimation and limited feedback is further discussed. Index Terms—OFDM, power allocation, bit allocation, amplifyandforward relaying, cooperative network. I.