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distance. However, let's assume that instead of wanting to minimize the total distance traveled to visit each desired destination, we wanted to minimize the total time needed to reach each destination. This goes beyond conventional optimization since travel time is inherently uncertain (traffic jams, time of day, etc.). As a result, to determine our optimal path we would want to use simulation - optimization to first understand the range of potential times it could take to go from one point to another (represented by a probability distribution in this case rather than a specific distance) and then optimize our travel decisions to identify the best path to follow taking that uncertainty into account.
25:
857:
is what is called a conventional optimization problem. That is, all the facts (distances between each destination point) needed to determine the optimal path to follow are known with certainty and the goal is to run through the possible travel choices to come up with the one with the lowest total
932:
copies of the system, randomly initialized, at different temperatures. Then, based on the
Metropolis criterion one exchanges configurations at different temperatures. The idea of this method is to make configurations at high temperatures available to the simulations at low temperatures and vice
933:
versa. This results in a very robust ensemble which is able to sample both low and high energy configurations. In this way, thermodynamical properties such as the specific heat, which is in general not well computed in the canonical ensemble, can be computed with great precision.
883:
of the function to be objectively minimized in which the function is nonlinearly transformed to allow for easier tunneling among regions containing function minima. Easier tunneling allows for faster exploration of sample space and faster convergence to a good solution.
2531:
1039:, a technique that attempts to solve a difficult optimization problem by initially solving a greatly simplified problem, and progressively transforming that problem (while optimizing) until it is equivalent to the difficult optimization problem.
633:
In both of these strategies, the set over which a function is to be optimized is approximated by polyhedra. In inner approximation, the polyhedra are contained in the set, while in outer approximation, the polyhedra contain the set.
234:
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methods. Finding the global minimum of a function is far more difficult: analytical methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.
502:
1110:
2476:
359:
182:
1354:. Kluwer Academic Publishers, Dordrecht, 1996. Now distributed by Springer Science and Business Media, New York. This book also discusses stochastic global optimization methods.
1339:
A.Neumaier, Complete Search in
Continuous Global Optimization and Constraint Satisfaction, pp. 271–369 in: Acta Numerica 2004 (A. Iserles, ed.), Cambridge University Press 2004.
2521:
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analysis and other generalizations, used in fitting model parameters to experimental data in chemistry, physics, biology, economics, finance, medicine, astronomy, engineering.
1300:
2592:
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729:
of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated
917:(MCMC) sampling methods more generally. The replica exchange method was originally devised by Swendsen, then extended by Geyer and later developed, among others, by
436:
308:
1429:, M. Brunato and F. Mascia, Reactive Search and Intelligent Optimization, Operations Research/Computer Science Interfaces Series, Vol. 45, Springer, November 2008.
416:
389:
288:
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of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function
1321:
507:
Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding
3196:
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1760:
1874:
1351:
2509:
1672:
The effective energy transformation scheme as a special continuation approach to global optimization with application to molecular conformation
1332:
1740:
2327:
3005:
2578:
1753:
3436:
2372:
1551:
Wenzel, W.; Hamacher, K. (1999-04-12). "Stochastic
Tunneling Approach for Global Minimization of Complex Potential Energy Landscapes".
190:
782:
that yield reliable results. Interval arithmetic helps find reliable and guaranteed solutions to equations and optimization problems.
2876:
2806:
2735:
1879:
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is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of
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on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
607:
2288:
1496:
Hamacher, K.; Wenzel, W. (1999-01-01). "Scaling behavior of stochastic minimization algorithms in a perfect funnel landscape".
1889:
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1080:
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1909:
1904:
951:
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Other approaches include heuristic strategies to search the search space in a more or less intelligent way, including:
441:
2675:
1451:
Hamacher, K (2006). "Adaptation in stochastic tunneling global optimization of complex potential energy landscapes".
1271:
1075:
620:
68:
46:
1261:
39:
2322:
2006:
1352:
Global
Optimization in Action - Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications
665:
1033:
Reactive search optimization (i.e. integration of sub-symbolic machine learning techniques into search heuristics)
2069:
1829:
1611:
Hansmann, Ulrich H.E. (1997). "Parallel tempering algorithm for conformational studies of biological molecules".
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1996:
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problems. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of
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2001:
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1899:
880:
528:
128:
1941:
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Marco
Falcioni and Michael W. Deem (1999). "A Biased Monte Carlo Scheme for Zeolite Structure Solution".
1126:, Proceedings of the 23rd Symposium on the Interface, American Statistical Association, New York, p. 156.
1085:
1009:
967:
534:
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1678:
For general considerations on the dimensionality of the domain of definition of the objective function:
766:, is a method developed by mathematicians since the 1950s and 1960s as an approach to putting bounds on
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2023:
1447:. Theory of Global Random Search. Mathematics and its applications. Kluwer Academic Publishers. 1991.
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minima or maxima. Finding an arbitrary local minimum is relatively straightforward by using classical
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version of parallel tempering: this is usually known as replica-exchange molecular dynamics or REMD.
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2180:
2140:
1856:
1369:
Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P. (1983-05-13). "Optimization by
Simulated Annealing".
1206:
Y. Sugita and Y. Okamoto (1999). "Replica-exchange molecular dynamics method for protein folding".
1017:
914:
601:
591:
33:
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1021:
831:
791:
2101:
1720:
For strategies allowing one to compare deterministic and stochastic global optimization methods
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L. Jaulin, M. Kieffer, O. Didrit, E. Walter (2001). Applied
Interval Analysis. Berlin: Springer.
1344:
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987:
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50:
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2013:
1991:
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simulations consists of an initial optimization of the energy of the system to be simulated.
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1974:
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8:
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1360:
E.R. Hansen (1992), Global
Optimization using Interval Analysis, Marcel Dekker, New York.
1063:
957:
820:
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722:
677:
669:
85:
1696:
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Hamacher, Kay (2005). "On stochastic global optimization of one-dimensional functions".
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1674:. Technical Report, Argonne National Lab., IL (United States), November 1996.
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1946:
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1535:
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1398:
1377:(4598). American Association for the Advancement of Science (AAAS): 671–680.
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850:
In this method, random simulations are used to find an approximate solution.
800:
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668:(MILP) problems, as well as to solve general, not necessarily differentiable
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is an umbrella term for optimization methods which iteratively refine a
2429:
1288:
On the Link
Between Gaussian Homotopy Continuation and Convex Envelopes
906:
585:
563:
2715:
1345:
Comparison of public-domain software for black box global optimization
1290:, In Lecture Notes in Computer Science (EMMCVPR 2015), Springer, 2015.
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2925:
2791:
2786:
2659:
2477:
The
Unreasonable Effectiveness of Mathematics in the Natural Sciences
1792:
1167:
706:
672:
problems. The use of cutting planes to solve MILP was introduced by
1347:. Optimization Methods & Software 13(3), pp. 203–226, 2000.
537:(e.g., minimize the number of character transformations in the tree)
3314:
3206:
3019:
2915:
2836:
2771:
2705:
1243:"Graduated Non-Convexity and Multi-Resolution Optimization Methods"
1135:
438:
is a (not necessarily convex) compact set defined by inequalities
3324:
3221:
2781:
2664:
1301:
Bayesian approach to global optimization: theory and applications
661:
229:{\displaystyle f:\Omega \subset \mathbb {R} ^{n}\to \mathbb {R} }
1190:"Parallel tempering: Theory, applications, and new perspectives"
1043:
3374:
3266:
3251:
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2801:
2745:
2725:
2710:
2532:
European Community on Computational Methods in Applied Sciences
2096:
1914:
656:
or objective function by means of linear inequalities, termed
524:
Typical examples of global optimization applications include:
187:
Given a possibly nonlinear and non-convex continuous function
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836:
Several exact or inexact Monte-Carlo-based algorithms exist:
2527:
International Council for Industrial and Applied Mathematics
1343:
M. Mongeau, H. Karsenty, V. Rouzé and J.-B. Hiriart-Urruty,
721:: the set of candidate solutions is thought of as forming a
2811:
2685:
2654:
1049:
785:
875:(STUN) is an approach to global optimization based on the
1205:
594:
and of many other models in the sciences and engineering
543:
and electrical circuit design (minimize the path length)
1368:
2600:
1775:
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with the full set at the root. The algorithm explores
2146:
Numerical methods for ordinary differential equations
1685:
Physica A: Statistical Mechanics and Its Applications
909:
method aimed at improving the dynamic properties of
444:
424:
397:
370:
319:
310:, the standard minimization problem can be given as
296:
269:
242:
193:
131:
102:
2522:
Société de Mathématiques Appliquées et Industrielles
2515:
Japan Society for Industrial and Applied Mathematics
2151:
Numerical methods for partial differential equations
1865:
1335:, Second Edition. Kluwer Academic Publishers, 2000.
2338:
1559:(15). American Physical Society (APS): 3003–3007.
625:The most successful general exact strategies are:
496:
430:
410:
383:
353:
302:
282:
255:
228:
176:
125:is equivalent to the minimization of the function
117:
1736:Introduction to global optimization by L. Liberti
497:{\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r}
3428:
1052:Indirect Optimization based on Self-Organization
936:
628:
321:
2510:Society for Industrial and Applied Mathematics
1550:
1495:
1259:
1111:Replica Monte Carlo simulation of spin glasses
1030:, combining global and local search strategies
839:
660:. Such procedures are popularly used to find
575:Object packing (configuration design) problems
2586:
1761:
1322:Global Optimization: Deterministic Approaches
1240:
1044:Response surface methodology-based approaches
2328:Supersymmetric theory of stochastic dynamics
1113:Physical Review Letters 57 : 2607–2609
683:
560:(e.g., of mechanical structures, buildings)
2593:
2579:
1768:
1754:
1058:, a sequential design strategy for global
531:(minimize the energy/free energy function)
1731:A. Neumaier’s page on Global Optimization
1624:
1564:
1509:
1280:
1260:Blake, Andrew; Zisserman, Andrew (1987).
1188:David J. Earl and Michael W. Deem (2005)
1149:
1002:with regard to a given measure of quality
811:) and their applications to the study of
354:{\displaystyle \min _{x\in \Omega }f(x),}
222:
208:
69:Learn how and when to remove this message
1682:
1610:
1450:
913:simulations of physical systems, and of
786:Methods based on real algebraic geometry
637:
614:
32:This article includes a list of general
960:, a generic probabilistic metaheuristic
861:
3429:
2574:
1749:
1286:Hossein Mobahi, John W. Fisher III.
1081:Multidisciplinary design optimization
970:capable of escaping from local minima
887:
825:
263:and the set of all global minimizers
177:{\displaystyle f(x):=(-1)\cdot g(x)}
18:
3415:Comparison of optimization software
1333:Introduction to Global Optimization
1316:Deterministic global optimization:
1241:Thacker, Neil; Cootes, Tim (1996).
1006:Swarm-based optimization algorithms
921:., Sugita and Okamoto formulated a
736:
13:
2602:Mathematical optimization software
1777:Industrial and applied mathematics
1422:For reactive search optimization:
425:
331:
297:
200:
38:it lacks sufficient corresponding
14:
3448:
3437:Deterministic global optimization
2007:Stochastic differential equations
1724:
1076:Deterministic global optimization
621:Deterministic global optimization
568:Mathematical problems (e.g., the
92:that attempts to find the global
2323:Supersymmetric quantum mechanics
1124:Computing Science and Statistics
666:mixed integer linear programming
23:
2205:Stochastic variational calculus
1997:Ordinary differential equations
1109:Swendsen RH and Wang JS (1986)
519:
2002:Partial differential equations
1875:Arbitrary-precision arithmetic
1459:(6). IOP Publishing: 944–950.
1293:
1253:
1234:
1199:
1182:
1129:
1116:
1103:
903:replica exchange MCMC sampling
817:sums-of-squares of polynomials
578:The starting point of several
461:
455:
345:
339:
218:
171:
165:
156:
147:
141:
135:
112:
106:
1:
3408:List of optimization software
1890:Interactive geometry software
1643:10.1016/s0009-2614(97)01198-6
1619:(1–3). Elsevier BV: 140–150.
1310:
1228:10.1016/S0009-2614(99)01123-9
1062:of black-box functions using
1014:social cognitive optimization
937:Heuristics and metaheuristics
629:Inner and outer approximation
1391:10.1126/science.220.4598.671
1096:
529:Protein structure prediction
7:
1942:Computational number theory
1905:Numerical-analysis software
1741:Free e-book by Thomas Weise
1705:10.1016/j.physa.2005.02.028
1583:10.1103/physrevlett.82.3003
1247:Vision Through Optimization
1086:Multiobjective optimization
1069:
1010:particle swarm optimization
840:Direct Monte-Carlo sampling
535:Computational phylogenetics
10:
3453:
1666:For continuation methods:
1091:Optimization (mathematics)
940:
891:
865:
855:traveling salesman problem
843:
829:
789:
740:
715:combinatorial optimization
687:
641:
618:
610:radiation therapy planning
541:Traveling salesman problem
391:and a global minimizer in
3402:
3353:
3305:
3186:
3157:
3093:
3004:
2900:
2753:
2744:
2639:
2608:
2540:
2502:
2486:
2448:
2400:
2348:Algebra of physical space
2213:
2171:
1965:
1927:
1815:Automated theorem proving
1783:
1473:10.1209/epl/i2006-10058-0
1453:Europhysics Letters (EPL)
1364:For simulated annealing:
2141:Numerical linear algebra
1691:. Elsevier BV: 547–557.
1613:Chemical Physics Letters
1606:For parallel tempering:
1440:For stochastic methods:
1208:Chemical Physics Letters
1018:multi-swarm optimization
915:Markov chain Monte Carlo
776:mathematical computation
684:Branch and bound methods
602:non-linear least squares
592:radio propagation models
1880:Finite element analysis
1830:Constraint satisfaction
1553:Physical Review Letters
1528:10.1103/physreve.59.938
1194:Phys. Chem. Chem. Phys.
1122:C. J. Geyer, (1991) in
1022:ant colony optimization
974:Evolutionary algorithms
952:Ant colony optimization
832:Stochastic optimization
792:Real algebraic geometry
431:{\displaystyle \Omega }
303:{\displaystyle \Omega }
236:with the global minima
53:more precise citations.
2435:Mathematical economics
2109:Multivariable calculus
1992:Differential equations
1835:Constraint programming
1825:Computational geometry
1037:Graduated optimization
988:Differential evolution
928:Essentially, one runs
498:
432:
412:
385:
355:
304:
284:
257:
230:
178:
119:
2388:Supersymmetry algebra
2373:Representation theory
2368:Renormalization group
2014:Differential geometry
1895:Optimization software
1867:Mathematical software
1299:Jonas Mockus (2013).
1263:Visual Reconstruction
1056:Bayesian optimization
638:Cutting-plane methods
615:Deterministic methods
556:Safety verification,
549:(e.g., analyzing the
499:
433:
413:
411:{\displaystyle X^{*}}
386:
384:{\displaystyle f^{*}}
356:
305:
285:
283:{\displaystyle X^{*}}
258:
256:{\displaystyle f^{*}}
231:
179:
120:
16:Branch of mathematics
2440:Mathematical finance
2425:Social choice theory
2340:Algebraic structures
2289:in quantum mechanics
2225:Analytical mechanics
2191:Stochastic processes
2163:Variational calculus
1975:Approximation theory
1900:Statistical software
998:trying to improve a
982:evolution strategies
873:Stochastic tunneling
868:Stochastic tunneling
862:Stochastic tunneling
819:. It can be used in
813:positive polynomials
778:and thus developing
764:interval computation
756:interval mathematics
709:design paradigm for
650:cutting-plane method
547:Chemical engineering
442:
422:
395:
368:
317:
294:
267:
240:
191:
129:
118:{\displaystyle g(x)}
100:
2415:Operations research
2284:Perturbation theory
2082:Multilinear algebra
2053:Functional analysis
1910:Numerical libraries
1842:Computational logic
1697:2005PhyA..354..547H
1635:1997CPL...281..140H
1575:1999PhRvL..82.3003W
1520:1999PhRvE..59..938H
1465:2006EL.....74..944H
1383:1983Sci...220..671K
1220:1999CPL...314..141S
1160:1999JChPh.110.1754F
1064:Bayesian statistics
958:Simulated annealing
821:convex optimization
752:Interval arithmetic
743:Interval arithmetic
670:convex optimization
564:Worst-case analysis
86:applied mathematics
82:Global optimization
2552:Mathematics portal
2449:Other applications
2173:Probability theory
2156:Validated numerics
2136:Numerical analysis
2029:Geometric analysis
2019:Differential forms
1852:Information theory
1320:R. Horst, H. Tuy,
1303:. Kluwer Academic.
1028:Memetic algorithms
1000:candidate solution
978:genetic algorithms
966:, an extension of
923:molecular dynamics
911:Monte Carlo method
899:Parallel tempering
894:Parallel tempering
888:Parallel tempering
877:Monte Carlo method
846:Monte Carlo method
826:Stochastic methods
809:real closed fields
772:measurement errors
719:state space search
580:molecular dynamics
558:safety engineering
513:local optimization
494:
428:
408:
381:
351:
335:
300:
280:
253:
226:
174:
115:
90:numerical analysis
3424:
3423:
3398:
3397:
2568:
2567:
2402:Decision sciences
2396:
2395:
2378:Spacetime algebra
2070:Harmonic analysis
2036:Dynamical systems
1980:Clifford analysis
1957:Discrete geometry
1923:
1922:
1498:Physical Review E
1435:978-0-387-09623-0
1324:, Springer, 1996.
780:numerical methods
760:interval analysis
570:Kepler conjecture
364:that is, finding
320:
79:
78:
71:
3444:
3297:Xpress NonLinear
3232:Gurobi Optimizer
3149:Xpress Optimizer
3114:Gurobi Optimizer
3085:Xpress NonLinear
3080:Xpress Optimizer
3035:Gurobi Optimizer
2996:Xpress Optimizer
2951:Gurobi Optimizer
2892:Xpress Optimizer
2822:Gurobi Optimizer
2751:
2750:
2595:
2588:
2581:
2572:
2571:
2353:Feynman integral
2336:
2335:
2296:Potential theory
2185:random variables
2075:Fourier analysis
2058:Operator algebra
1985:Clifford algebra
1937:Computer algebra
1863:
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1756:
1747:
1746:
1716:
1662:
1628:
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1513:
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1331:and N.V. Thoai,
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990:, a method that
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943:Metaheuristic
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853:Example: The
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747:Set inversion
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664:solutions to
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59:December 2013
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3406:
3390:Xpress Kalis
3371:CP Optimizer
3306:
2731:Xpress Mosel
2681:GNU MathProg
2609:Data formats
2558: /
2554: /
2544:
2420:Optimization
2383:Superalgebra
2242:Field theory
2215:Mathematical
2193: /
2041:Chaos theory
2024:Gauge theory
1952:Graph theory
1847:Cryptography
1719:
1688:
1684:
1677:
1670:Zhijun Wu.
1665:
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968:local search
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797:Real algebra
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654:feasible set
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586:Spin glasses
551:Gibbs energy
523:
520:Applications
512:
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363:
186:
81:
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65:
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3380:Mathematica
3330:Mathematica
3168:Mathematica
3129:Mathematica
3050:Mathematica
2966:Mathematica
2847:Mathematica
2817:GLPK/GLPSOL
2701:Mathematica
2616:Mathematica
2560:topics list
2494:Mathematics
2410:Game theory
2311:Topological
2277:Topological
2272:Statistical
2235:Hamiltonian
996:iteratively
964:Tabu search
723:rooted tree
51:introducing
2466:Psychology
2430:Statistics
2230:Lagrangian
1857:Statistics
1793:Algorithms
1327:R. Horst,
1311:References
1196:, 7, 3910
907:simulation
34:references
2660:APMonitor
2471:Sociology
2461:Chemistry
2257:Effective
2252:Conformal
2247:Classical
2119:Geometric
2092:Geometric
1713:0378-4371
1651:0009-2614
1591:0031-9007
1544:119096368
1536:1063-651X
1489:250761754
1481:0295-5075
1399:0036-8075
1097:Footnotes
992:optimizes
707:algorithm
486:…
465:⩾
426:Ω
404:∗
377:∗
332:Ω
329:∈
298:Ω
276:∗
249:∗
219:→
204:⊂
201:Ω
160:⋅
151:−
3431:Category
3315:ANTIGONE
3207:ANTIGONE
3097:, MISOCP
3020:ANTIGONE
2916:ANTIGONE
2887:SYMPHONY
2837:Lp_solve
2772:ANTIGONE
2706:MiniZinc
2641:Modeling
2546:Category
2195:analysis
2114:Exterior
2087:Exterior
1967:Analysis
1929:Discrete
1803:analysis
1659:14137470
1407:17813860
1176:13963102
1070:See also
881:sampling
727:branches
711:discrete
705:) is an
418:; where
3325:Couenne
3222:Couenne
3190:, MINLP
3161:, MISDP
3008:, MIQCP
2746:Solvers
2665:ECLiPSe
2556:outline
2487:Related
2456:Biology
2306:Bosonic
2267:Quantum
2217:physics
2183: (
1915:Solvers
1693:Bibcode
1631:Bibcode
1599:5113626
1571:Bibcode
1516:Bibcode
1461:Bibcode
1379:Bibcode
1371:Science
1216:Bibcode
1156:Bibcode
1008:(e.g.,
976:(e.g.,
905:, is a
703:B&B
662:integer
47:improve
3375:Gecode
3267:NLPQLP
3252:MIDACO
2941:FortMP
2904:, MIQP
2877:SoPlex
2802:FortMP
2726:TOMLAB
2711:OptimJ
2129:Vector
2124:Tensor
2102:Vector
2097:Tensor
1798:design
1711:
1657:
1649:
1597:
1589:
1542:
1534:
1487:
1479:
1433:
1415:205939
1413:
1405:
1397:
1270:
1174:
731:bounds
36:, but
3385:JaCoP
3369:CPLEX
3365:Comet
3335:LINDO
3320:BARON
3292:WORHP
3282:SNOPT
3272:NPSOL
3257:MINOS
3242:LINDO
3237:IPOPT
3217:BARON
3202:APOPT
3173:MOSEK
3134:MOSEK
3119:LINDO
3109:CPLEX
3060:MOSEK
3055:MINOS
3045:LINDO
3040:IPOPT
3030:CPLEX
3015:APOPT
2976:MOSEK
2971:MINOS
2961:LINDO
2956:IPOPT
2946:HiGHS
2936:CPLEX
2911:APOPT
2862:MOSEK
2857:MINTO
2852:MINOS
2832:LINDO
2827:HiGHS
2797:CPLEX
2767:APOPT
2736:ZIMPL
2721:Pyomo
2691:LINDO
2671:Gekko
2650:AIMMS
2643:tools
2262:Gauge
1655:S2CID
1621:arXiv
1595:S2CID
1561:arXiv
1540:S2CID
1506:arXiv
1485:S2CID
1411:S2CID
1172:S2CID
1146:arXiv
954:(ACO)
762:, or
600:like
509:local
3340:SCIP
3277:SCIP
3247:LOQO
3144:SCIP
3124:LOQO
3095:SOCP
3070:SCIP
2991:SCIP
2872:SCIP
2842:LOQO
2812:GLOP
2759:MILP
2716:PuLP
2686:JuMP
2676:GAMS
2667:-CLP
2655:AMPL
1709:ISSN
1647:ISSN
1587:ISSN
1532:ISSN
1477:ISSN
1431:ISBN
1403:PMID
1395:ISSN
1268:ISBN
1050:IOSO
1020:and
980:and
815:and
803:and
770:and
745:and
713:and
676:and
658:cuts
648:The
608:IMRT
88:and
3262:NAG
3197:AOA
3188:NLP
3178:NAG
3159:SDP
3139:NAG
3065:NAG
3006:QCP
2981:NAG
2931:CLP
2926:CBC
2867:NAG
2807:GCG
2792:CBC
2787:CLP
2782:BCP
2696:OPL
2631:sol
2621:MPS
1701:doi
1689:354
1639:doi
1617:281
1579:doi
1524:doi
1469:doi
1387:doi
1375:220
1224:doi
1212:314
1192:,
1164:doi
1142:110
774:in
701:or
322:min
290:in
184:.
3433::
3355:CP
3307:GO
2902:QP
2757:,
2755:LP
2626:nl
1707:.
1699:.
1687:.
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1645:.
1637:.
1629:.
1615:.
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1500:.
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