Daniel Solow
Case Western Reserve University, Operations, Faculty Member
This paper addresses an area of complex systems that appears to have been largely overlooked. While there is a significant amount of work dealing with self-organizationand its associated emergent propertiesthere is almost no literature... more
This paper addresses an area of complex systems that appears to have been largely overlooked. While there is a significant amount of work dealing with self-organizationand its associated emergent propertiesthere is almost no literature on the role and impact of ...
This research presents a new constrained optimization approach for solving systems of nonlinear equations. Particular advantages are realized when all of the equations are convex. For example, a global algorithm for finding the zero of a... more
This research presents a new constrained optimization approach for solving systems of nonlinear equations. Particular advantages are realized when all of the equations are convex. For example, a global algorithm for finding the zero of a convex real-valued function of one variable is developed. If the algorithm terminates finitely, then either the algorithm has computed a zero or determined that none exists; if an infinite sequence is generated, either that sequence converges to a zero or again no zero exists. For solving n-dimensional convex equations, the constrained optimization algorithm has the capability of determining that the system of equations has no solution. Global convergence of the algorithm is established under weaker conditions than previously known and, in this case, the algorithm reduces to Newton’s method together with a constrained line search at each iteration. It is also shown how this approach has led to a new algorithm for solving the linear complementarity problem.
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In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are ‘shrinking’ to a point.... more
In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are ‘shrinking’ to a point. This paper proposes a new method for shrinking the simplexes. It is shown that under certain conditions, the function whose fixed point is sought may be used to control this shrinking process. A computational method for implementing these ideas is also suggested and several examples are solved using this approach.
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Whereas much of the previous research in complex systems has focused on emergent properties resulting from self-organization of the individual agents that make up the system, this article studies one vital role of central organization. In... more
Whereas much of the previous research in complex systems has focused on emergent properties resulting from self-organization of the individual agents that make up the system, this article studies one vital role of central organization. In particular, four factors are conjectured to be key in determining the optimal amount of central control. To validate this hypothesis, these factors are represented as controllable parameters in a mathematical model. For different combinations of parameter values, the optimal amount of central control is found, either analytically or by computer simulation. The model is shown to provide results that match well with the level of control found across a broad spectrum of specific complex systems. This model also provides general guidelines as to how combinations of these factors affect the desirable level of control and specific guidelines for selecting and evaluating leaders. These results indicate that all of these factors, though not exhaustive, should be considered carefully when attempting to determine the amount of control that is best for a system. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008
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Abstract: An open question pertaining to the simplex algorithm is where phase 1 terminates on the feasible region. Here, computer simulations support the conjecture that phase 1 terminates at a feasible point geometrically close to the... more
Abstract: An open question pertaining to the simplex algorithm is where phase 1 terminates on the feasible region. Here, computer simulations support the conjecture that phase 1 terminates at a feasible point geometrically close to the starting point. This observation leads to a ...
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This paper reports the development of a new algorithm for solving the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints). The approach is based on the... more
This paper reports the development of a new algorithm for solving the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints). The approach is based on the complementary pivoting algorithms which ...
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ABSTRACT In this paper, we evaluate the effectiveness of policies for assigning interdependent workers to teams. Using a computational simulation, we contrast distributing workers equitably across teams based on prior individual... more
ABSTRACT In this paper, we evaluate the effectiveness of policies for assigning interdependent workers to teams. Using a computational simulation, we contrast distributing workers equitably across teams based on prior individual performance with policies that distribute workers based on how well people work together. First, we test a policy that clusters workers into teams by finding natural breakpoints among them where their mutual support is weak. Then we test two other policies that both protect the strongest interdependent core of high performers but differ in that one policy separates workers who give little support to interdependent partners and the other separates workers who receive little support from their partners. All three policies outperform the equitable-distribution approach in some circumstances. We make recommendations to managers for harnessing interdependence when forming teams, whether the managers are familiar or unfamiliar with how well their people work together.
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Abstract. Various methods, such as address-calculation sorts, distribution counting sorts, radix sorts, and bucket sorts, use the values of the numbers being sorted to increase efficiency but do so at the expense of requiring additional... more
Abstract. Various methods, such as address-calculation sorts, distribution counting sorts, radix sorts, and bucket sorts, use the values of the numbers being sorted to increase efficiency but do so at the expense of requiring additional storage space. In this paper, a specific ...
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In the past decade, several complementary pivot algorithms have been developed to search for fixed points of certain functions and point to set maps on unbounded regions. This paper develops a structure (called decomposability), which,... more
In the past decade, several complementary pivot algorithms have been developed to search for fixed points of certain functions and point to set maps on unbounded regions. This paper develops a structure (called decomposability), which, when present, enables one to work in a lower dimensional space when solving these problems. Several examples of where this structure arises in applications are presented. It is shown that under suitable circumstances, the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints) may be formulated as a decomposèble fixed point problem. At the same time, an approximation technique is developed to potentially improve the efficiency of the complementary pivot algorithms.
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This article investigates when a growing team benefits from being divided and how complex interactions among workers and management impact this decision. The proposed model—a modification of Kauffman's NK model—has the property that team... more
This article investigates when a growing team benefits from being divided and how complex interactions among workers and management impact this decision. The proposed model—a modification of Kauffman's NK model—has the property that team performance decreases as the size of the team increases. Analytical results and computer simulations show how team size, the amount of supervision, worker performance, interaction among employees, relationships between management and labor, and leadership skill affect when a team should be split. © 2007 Wiley Periodicals, Inc. Complexity 12: 54–70, 2007
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... On the challenge of developing a formal mathematical theory for establishing emergence in complex systems. Daniel Solow. Article first published online: 25 JAN 2001. ... More content like this. Find more content: like this article.... more
... On the challenge of developing a formal mathematical theory for establishing emergence in complex systems. Daniel Solow. Article first published online: 25 JAN 2001. ... More content like this. Find more content: like this article. Find more content written by: Daniel Solow. ...
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A descent algorithm simultaneously capable of solving linear programming, piecewise linear convex minimization, and the linear complementarity problem is developed. Con-ditions are given under which a solution can be found in a finite... more
A descent algorithm simultaneously capable of solving linear programming, piecewise linear convex minimization, and the linear complementarity problem is developed. Con-ditions are given under which a solution can be found in a finite number of iterations using the ...
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This paper is concerned with the development of an improvement algorithm for the Linear Complementarity Problem (LCP). Our approach to find a solution to LCP is to solve the equivalent Constrained Optimization Problem (COP) of maximizing... more
This paper is concerned with the development of an improvement algorithm for the Linear Complementarity Problem (LCP). Our approach to find a solution to LCP is to solve the equivalent Constrained Optimization Problem (COP) of maximizing the sum of the minimum of each complementary pair of variables, subject to the constraints that each such minimum is nonpositive.The algorithm, ascent in nature, is similar to the simplex method in the sense that it moves between basic points of an associated system of linear equations. These basic points are feasible to our COP whose objective function is piecewise linear and concave. Classes of matrices are characterized for which our algorithm processes LCP for every right hand side vector and every matrix in the class. A computational study shows that our algorithm is clearly superior to a previos improvement algorithm. Computational comparisons with Lemke's well known algorithm are also presented.
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An academic directory and search engine.
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An academic directory and search engine.
Truckload carriers are constantly faced with the problem of shipping full truckloads of goods at minimum cost between pairs of cities or customers, using a fleet of trucks located at one or more depots. In this paper, a new... more
Truckload carriers are constantly faced with the problem of shipping full truckloads of goods at minimum cost between pairs of cities or customers, using a fleet of trucks located at one or more depots. In this paper, a new branch-and-bound algorithm for solving an integer-...
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... How to read and do proofs: An introduction to mathematical thought process. Post a Comment. CONTRIBUTORS: Author: Solow, Daniel. PUBLISHER: J. Wiley (New York). SERIES TITLE: YEAR: 1982. PUB TYPE: Book (ISBN 0471866458 [pbk]).... more
... How to read and do proofs: An introduction to mathematical thought process. Post a Comment. CONTRIBUTORS: Author: Solow, Daniel. PUBLISHER: J. Wiley (New York). SERIES TITLE: YEAR: 1982. PUB TYPE: Book (ISBN 0471866458 [pbk]). VOLUME/EDITION: ...
ROPAS Library. How to Read and Do Proofs (2nd Ed.). Daniel Solow. John Wiley & Sons, ISBN: 0471453005 This book is at Kwang's library. Available as of 2011-04-14. is going to this book. [ List ]. XHTML. © Programming Research... more
ROPAS Library. How to Read and Do Proofs (2nd Ed.). Daniel Solow. John Wiley & Sons, ISBN: 0471453005 This book is at Kwang's library. Available as of 2011-04-14. is going to this book. [ List ]. XHTML. © Programming Research Laboratory, Seoul National University. ...