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16
An InteriorPoint Algorithm For Nonconvex Nonlinear Programming
 COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
, 1997
"... The paper describes an interiorpoint algorithm for nonconvex nonlinear programming which is a direct extension of interiorpoint methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the mer ..."
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Cited by 144 (13 self)
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The paper describes an interiorpoint algorithm for nonconvex nonlinear programming which is a direct extension of interiorpoint methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models.
Benchmarking Optimization Software with COPS
, 2000
"... 1 Introduction 1 Testing Methods 2 1 Largest Small Polygon 3 2 Distribution of Electrons on a Sphere 5 3 Hanging Chain 7 4 Shape Optimization of a Cam 9 5 Isometrization of ffpinene 11 6 Marine Population Dynamics 13 7 Flow in a Channel 16 8 Robot Arm 18 9 Particle Steering 21 10 Goddard Rocket 23 ..."
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Cited by 23 (0 self)
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1 Introduction 1 Testing Methods 2 1 Largest Small Polygon 3 2 Distribution of Electrons on a Sphere 5 3 Hanging Chain 7 4 Shape Optimization of a Cam 9 5 Isometrization of ffpinene 11 6 Marine Population Dynamics 13 7 Flow in a Channel 16 8 Robot Arm 18 9 Particle Steering 21 10 Goddard Rocket 23 11 Hang Glider 26 12 Catalytic Cracking of Gas Oil 29 13 Methanol to Hydrocarbons 31 14 Catalyst Mixing 33 15 ElasticPlastic Torsion 35 16 Journal Bearing 37 17 Minimal Surface with Obstacle 39 Acknowledgments 41 References 41 ii Benchmarking Optimization Software with COPS by Elizabeth D. Dolan and Jorge J. Mor'e Abstract We describe version 2.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the LANCELOT, LOQO, MINOS, and SNOPT solvers on these problems. Introduction The COPS [5] test set provides a modest selection of difficult nonlinearly constrai...
COPS: LargeScale Nonlinearly Constrained Optimization Problems
"... 1 1 Introduction 1 2 Largest Small Polygon (Gay [8]) 3 3 Distribution of Electrons on a Sphere (Vanderbei [13]) 5 4 Sawpath Tracking (Vanderbei [13]) 7 5 Hanging Chain (H. Mittelmann, private communication) 10 6 Shape Optimization of a Cam (Anitescu and Serban [1]) 12 7 Isometrization of ffpinene ( ..."
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Cited by 18 (1 self)
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1 1 Introduction 1 2 Largest Small Polygon (Gay [8]) 3 3 Distribution of Electrons on a Sphere (Vanderbei [13]) 5 4 Sawpath Tracking (Vanderbei [13]) 7 5 Hanging Chain (H. Mittelmann, private communication) 10 6 Shape Optimization of a Cam (Anitescu and Serban [1]) 12 7 Isometrization of ffpinene (MINPACK2 test problems [3]) 15 8 Marine Population Dynamics (Rothschild et al. [11]) 18 9 Flow in a Channel (MINPACK2 test problems [3]) 21 10 Noninertial Robot Arm (Vanderbei [13]) 24 11 Linear Tangent Steering (Betts, Eldersveld, and Huffman [4]) 29 12 Goddard Rocket (Betts, Eldersveld, and Huffman [4]) 32 13 Hang Glider (Betts, Eldersveld, Huffman [4]) 35 14 Implementation of COPS in C 38 References 43 ii COPS: LargeScale Nonlinearly Constrained Optimization Problems Alexander S. Bondarenko, David M. Bortz, and Jorge J. Mor'e Abstract We have started the development of COPS, a collection of largescale nonlinearly Constrained Optimization ProblemS. The primary purpose of this col...
Benchmarking optimization software with cops 3.0
 MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY
, 2004
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On conway’s thrackle conjecture
 Proc. 11th ACM Symp. on Computational Geometry
, 1995
"... A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle can ..."
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Cited by 12 (2 self)
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A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About forty years ago, J. H. Conway conjectured that the number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many edges as vertices. Some related problems and generalizations are also considered. 1
Automatic Differentiation of Nonlinear AMPL Models
 IN AUTOMATIC DIFFERENTIATION OF ALGORITHMS: THEORY, IMPLEMENTATION, AND APPLICATION
, 1991
"... We describe favorable experience with automatic differentiation of mathematical programming problems expressed in AMPL, a modeling language for mathematical programming. Nonlinear expressions are translated to loopfree code, which makes analytically correct gradients and Jacobians particularly easy ..."
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Cited by 10 (9 self)
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We describe favorable experience with automatic differentiation of mathematical programming problems expressed in AMPL, a modeling language for mathematical programming. Nonlinear expressions are translated to loopfree code, which makes analytically correct gradients and Jacobians particularly easy to compute  static storage allocation suffices. The nonlinear expressions may either be interpreted or, to gain some execution speed, converted to Fortran or C.
The Largest Small Octagon
"... Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to nd the octagon with unit diameter and largest area. This proves the rst open case of a conjecture of Graham (1975). Keywords: octagon, area, diameter, thrackleation, quadratic programming ..."
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Cited by 7 (3 self)
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Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to nd the octagon with unit diameter and largest area. This proves the rst open case of a conjecture of Graham (1975). Keywords: octagon, area, diameter, thrackleation, quadratic programming. Resume On utilise la trackleation des graphes et l'optimisation globale de programmation quadratique a contraintes quadratiques pour determiner l'octogone de diametre unitaire de surface maximale. Ceci prouve le premier cas ouvert d'une conjecture de Graham (1975). Mots clefs: octogone, surface, diametre, trackleation, programmation quadratique. 1
Isodiametric Problems for Polygons
 Discrete and Computational Geometry
"... Abstract. The maximal area of a polygon with n = 2m edges and unit diameter is not known when m ≥ 5, nor is the maximal perimeter of a convex polygon with n = 2 m edges and unit diameter known when m ≥ 4. We construct improved polygons in both problems, and show that the values we obtain cannot be i ..."
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Cited by 2 (0 self)
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Abstract. The maximal area of a polygon with n = 2m edges and unit diameter is not known when m ≥ 5, nor is the maximal perimeter of a convex polygon with n = 2 m edges and unit diameter known when m ≥ 4. We construct improved polygons in both problems, and show that the values we obtain cannot be improved for large n by more than c1/n 3 in the area problem and c2/n 5 in the perimeter problem, for certain constants c1 and c2. 1.
A Collection of LargeScale Nonlinearly Constrained Optimization Test Problems.
"... This paper describes a set of nonlinearly constrained optimization problems that can be used to test and develop optimization algorithms for nonlinearly constrained problems. We drew these test problems from a wide variety of sources, including some of the already existing collections, such as the A ..."
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Cited by 1 (0 self)
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This paper describes a set of nonlinearly constrained optimization problems that can be used to test and develop optimization algorithms for nonlinearly constrained problems. We drew these test problems from a wide variety of sources, including some of the already existing collections, such as the AMPL problems on Vanderbei's web site [15] and MINPACK2 collection [3]. We chose the problems for this collection that are related to various applications (e.g. fluid dynamics, optimal shape design, population dynamics) and/or interesting. In the following section 2, each problem has a short derivation and description of the problem, providing the information in Table 1.1, followed by the general comments on the problem's specific features and difficulties. Then we provide the results of the computational Table 1.1: Description of test problems