Estimated H-index: 8. We introduce a new method for solving box-constrained mixed-integer polynomial problems to global optimality. The approach, a specialized branch-and-bound algorithm, is based on the computation of lower bounds provided by the minimization of separable underestimators of the polynomial objective function.
The underestimators are the novelty of the approach because the standard approaches in global optimization are based on convex relaxations. Thanks to the fact that only simple bound constraints Quadratic reformulations of nonlinear binary optimization problems. Martin Anthony 17 Estimated H-index: Estimated H-index: 5. Very large nonlinear unconstrained binary optimization problems arise in a broad array of applications.
Several exact or heuristic techniques have proved quite successful for solving many of these problems when the objective function is a quadratic polynomial. However, no similarly efficient methods are available for the higher degree case. Since high degree objectives are becoming increasingly important in certain application areas, such as computer vision, various techniques have been recently Efficient minimization of higher order submodular functions using monotonic Boolean functions. Srikumar Ramalingam 20 Estimated H-index: Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision and many others.
On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the Francisco Chicano 16 Estimated H-index: Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For k-bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time.
These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to Francaise Rech. Remarks on Motinori Goto's papers on Boolean equations.
- On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint | SpringerLink.
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Roumaine Math. Roumaine 7 55 , Hammer Minimization of switching circuits in actual operation. On solving Boolean equations in the theory of graphs. Axiomatization of certain problems of minimization. Studia Logica 20 , Belgrade 6 20 , On Tohma's decomposition of logical functions. IEEE Trans. Electronic Computers EC , Irredundant solutions of Boolean and pseudo-Boolean equations. A-B , Hammer Extensions of pseudo-Boolean Programming. Vesnik Beograd 4 19 , Hammer A pseudo-Boolean approach to matching problems in graphs with applications to assignment and transportation problems.
Pdf Pseudo-Boolean Methods For Bivalent Programming
Hammer A pseudo-Boolean viewpoint on systems of representatives. Applicationes Math. Hammer Pseudo-Boolean Programming. Operations Res. On functions and equations in distributive lattices.
Reduction of bivalent maximization to the quadratic case
Edinburgh Math. Fabian, Gh. Weisz Rezolvarea problemelor de programare pseudo-booleana liniara cu ajutorul unui calculator electronic. On elimination in Boolean algebra. Hitotsubashi J. Arts and Sci.
Irredundant optimization of pseudo-Boolean functions. Optimization Theory Appl. An axiomatic approach to pseudo-Boolean programming. Vesnik Beograd 7 22 , Boolean equations for the chromatic decomposition of graphs. Bucuresti ser. Francaise Informat.
On reproductive solutions of Boolean equations. Belgrade 10 24 , Logique, Automatique, Informatique. Editura Academiei R. Romania, Bucuresti , On Boolean matrix equations. Cunkle Rings in Boolean algebras. Discrete Math. An algebraic approach to Boolean equations.
Computers C , Testing Boolean identities.
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CRM, July Local properties of Boolean functions. Extremal solutions of Boolean equations. Gavrilov editor , Teoria avtomatov, Iz-stvo Nauka, Moskva , Square roots and functional decomposition of Boolean functions. On the range of a Boolean transformation. Belgrade 19 33 , Melter Geometry of 3-rings.
Colloquia Math. Systems of linear Boolean equations. Belgrade 22 36 , Injectivity domains of Boolean transformations. Cazanescu Independent sets and kernels in graphs and hypergraphs. Kinshasa 4 , On reproductive solutions of arbitrary equations. Belgrade 24 38 Ghilezan Interpolation formulas over finite sets. Belgrade 25 39 , Brown Consequences, consistency and independence in Boolean algebras. Notre Dame J.
Formal Logic 22 , Fixpoints of lattice and Boolean transformations. Cuza Iasi 26 , Melter Characterizations of Boolean functions. Cuza Iasi 28 , Melter Generalized inverses of Boolean functions. Melter A measure of central tendency for Boolean algebras. Cuza Iasi 27 , The download pseudo boolean methods for called to capture reported 's, as, delta.
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