7,472 research outputs found
Sufficient optimality criteria and duality for multiobjective variational control problems with G-type I objective and constraint functions
In the paper, we introduce the concepts of G-type I and generalized G-type I
functions for a new class of nonconvex multiobjective variational control problems. For
such nonconvex vector optimization problems, we prove sufficient optimality conditions for
weakly efficiency, efficiency and properly efficiency under assumptions that the functions
constituting them are G-type I and/or generalized G-type I objective and constraint functions.
Further, for the considered multiobjective variational control problem, its dual multiobjective
variational control problem is given and several duality results are established under
(generalized) G-type I objective and constraint functions
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
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Singular Lagrangian Systems on Jet Bundles
The jet bundle description of time-dependent mechanics is revisited. The
constraint algorithm for singular Lagrangians is discussed and an exhaustive
description of the constraint functions is given. By means of auxiliary
connections we give a basis of constraint functions in the Lagrangian and
Hamiltonian sides. An additional description of constraints is also given
considering at the same time compatibility, stability and second-order
condition problems. Finally, a classification of the constraints in first and
second class is obtained using a cosymplectic geometry setting. Using the
second class constraints, a Dirac bracket is introduced, extending the
well-known construction by Dirac.Comment: 65 pages. LaTeX fil
Optimal design of solidification processes
An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem
On singular Lagrangians affine in velocities
The properties of Lagrangians affine in velocities are analyzed in a
geometric way. These systems are necessarily singular and exhibit, in general,
gauge invariance. The analysis of constraint functions and gauge symmetry leads
us to a complete classification of such Lagrangians.Comment: AMSTeX, 22 page
Quantum deformation of the Dirac bracket
The quantum deformation of the Poisson bracket is the Moyal bracket. We
construct quantum deformation of the Dirac bracket for systems which admit
global symplectic basis for constraint functions. Equivalently, it can be
considered as an extension of the Moyal bracket to second-class constraints
systems and to gauge-invariant systems which become second class when
gauge-fixing conditions are imposed.Comment: 18 pages, REVTe
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