Deterministic Global Optimization: Theory, Methods and ApplicationsSpringer Science & Business Media, 2013. gada 9. marts - 742 lappuses The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications. |
No grāmatas satura
1.–5. rezultāts no 38.
viii. lappuse
... Univariate Polynomial Problems 3.11 Additional Properties of the Lagrange Function 3.12 The GOP in a Branch and Bound Framework 3.13 Reformulation Of The Relaxed Dual As A Single MILP Problem 3.14 A Linear Branching Scheme for the GOP ...
... Univariate Polynomial Problems 3.11 Additional Properties of the Lagrange Function 3.12 The GOP in a Branch and Bound Framework 3.13 Reformulation Of The Relaxed Dual As A Single MILP Problem 3.14 A Linear Branching Scheme for the GOP ...
28. lappuse
... function and / or constraints . This approach classifies the nonconvexities as special structure ( e.g. , bilinear , signomial , univariate ) or generic structure and is based on convex relaxations and a branch and bound framework ...
... function and / or constraints . This approach classifies the nonconvexities as special structure ( e.g. , bilinear , signomial , univariate ) or generic structure and is based on convex relaxations and a branch and bound framework ...
46. lappuse
... functions is a very challenging problem by itself . 2.4.1 Convex Envelope of a Concave Function over a Polytope The ... Univariate Function The convex envelope of a univariate concave function f ( x ) over [ x1‚x ' ] is its linearization ...
... functions is a very challenging problem by itself . 2.4.1 Convex Envelope of a Concave Function over a Polytope The ... Univariate Function The convex envelope of a univariate concave function f ( x ) over [ x1‚x ' ] is its linearization ...
50. lappuse
... Univariate Functions For products of univariate functions that are twice continuously differentiable , the following two theorems ( Maranas and Floudas ( 1995 ) ) provide the basis for the underestimation and establish the convex ...
... Univariate Functions For products of univariate functions that are twice continuously differentiable , the following two theorems ( Maranas and Floudas ( 1995 ) ) provide the basis for the underestimation and establish the convex ...
51. lappuse
... functions ( f1g ( y ) ) + ø ( g1ƒ ( x ) ) – ƒ1g and ( fg ( y ) ) + þ ( g1ƒ ( x ) ) – ƒʊg are convex as the sum of the convex envelopes of univariate functions . Since the maximum of two convex functions is a convex function as well ...
... functions ( f1g ( y ) ) + ø ( g1ƒ ( x ) ) – ƒ1g and ( fg ( y ) ) + þ ( g1ƒ ( x ) ) – ƒʊg are convex as the sum of the convex envelopes of univariate functions . Since the maximum of two convex functions is a convex function as well ...
Saturs
1 | |
THE GOP APPROACH IMPLEMENTATION AND COMPUTATIONAL STUDIES | 141 |
THE GOP APPROACH IN BILEVEL LINEAR AND QUADRATIC PROBLEMS | 173 |
DISTRIBUTED IMPLEMENTATION | 243 |
Signomial Problems | 257 |
COMPUTATIONAL STUDIES | 289 |
FROM BICONVEX TO GENERAL TWICE DIFFERENTIABLE NLPS | 309 |
THEORY315 | 315 |
THE ABB APPROACH IN PEPTIDE DOCKING | 481 |
THE ABB APPROACH IN BATCH DESIGN UNDER UNCERTAINTY | 507 |
THE aBB APPROACH IN PARAMETER ESTIMATION | 543 |
Nonlinear and MixedInteger Optimization | 571 |
THE SMINαBB APPROACH THEORY AND COMPUTATIONS | 587 |
THE GMINaBB APPROACH THEORY AND COMPUTATIONS | 617 |
Nonlinear Constrained Systems of Equations | 641 |
LOCATING ALL HOMOGENEOUS AZEOTROPES | 667 |
THE aBB FOR CONSTRAINED TWICE DIFFERENTIABLE NLPS THEORY | 333 |
COMPUTATIONAL STUDIES OF THE ABB APPROACH | 377 |
GLOBAL OPTIMIZATION IN MICROCLUSTERS | 403 |
THE ABB APPROACH IN MOLECULAR STRUCTURE PREDICTION | 435 |
References | 699 |
xiii | 736 |
Citi izdevumi - Skatīt visu
Deterministic Global Optimization: Theory, Methods and Applications Christodoulos A. Floudas Priekšskatījums nav pieejams - 2010 |
Bieži izmantoti vārdi un frāzes
Adjiman azeotropes bilinear terms binary variables bound updates bounding function branch and bound Chapter concave function connected variables convergence convex envelope convex functions convex lower bounding convex relaxation convex set convex underestimators corresponding defined dihedral angles eigenvalue equation Figure formulation fractional function f(x Gibbs free energy global minimum global optimization algorithm global optimization approach global solution GMIN-aBB GOP algorithm Hessian matrix integer interval iteration Lagrange function linear Maranas and Floudas maximum separation methods MILP minimization MINLP node nonconvex terms nonlinear number of iterations objective function obtained optimization problem parameters peptide potential energy primal problem programming problem properties quadratic qualifying constraints relaxed dual problem relaxed dual subproblems shift matrix solved Table tangent plane Theorem total number upper bound variable bounds vector