Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Regularity and strong sufficient optimality conditions in differentiable optimization problems
1993
This paper studies the metric regularity of multivalued functions on Banach spaces, tangential approximations of the feasible set and strong sufficient optimality conditions of a parametrized optimization problem minimize The results are applied to the tangent approximations and the local stability properties of solutions of this perturbed optimization problem.
Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation
1992
Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.
Sensitivity analysis for optimal shape design problems
1989
Various methods for performing the sensitivity analysis in solving optimal shape design problems are outlined. The methods are illustrated in detail in the finite setting of a unilateral boundary value problem of the Dirichlet-Signorini type. The methods are compared in several numerical examples.
Team Theory and Person-by-Person Optimization with Binary Decisions
2012
In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we prese…
Distributed <inline-formula> <tex-math notation="TeX">$n$</tex-math></inline-formula>-Player Approachability and Consensus in…
2015
We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that makes the grand …
The solution of a ‘ fixed-target’—model by an approach of system analysis
1974
Abstract A general approach fur economic systems is combined with a concrete ‘ fixed-target’—model. The consideration of convergence leads—under conditions of a stable solution and two targets—to the result that five numerical restrictions must be recognized when treating the two instruments. Generalizations of the discussed illustrative model are possible.
How to simulate normal data sets with the desired correlation structure
2010
The Cholesky decomposition is a widely used method to draw samples from multivariate normal distribution with non-singular covariance matrices. In this work we introduce a simple method by using singular value decomposition (SVD) to simulate multivariate normal data even if the covariance matrix is singular, which is often the case in chemometric problems. The covariance matrix can be specified by the user or can be generated by specifying a subset of the eigenvalues. The latter can be an advantage for simulating data sets with a particular latent structure. This can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their app…
Statistical validation of rival models for observable stochastic process and its identification
2011
In this paper, for statistical validation of rival (analytical or simulation) models collected for modeling observable process in stochastic system (say, transportation or service system), a uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of multivariate normal populations (compared with respect to their means) are different and unknown. The test makes use of an invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and thresho…
Cross-Efficiency in Fuzzy Data Envelopment Analysis (FDEA): Some Proposals
2013
Different techniques have been proposed in the literature to rank decision making units (DMUs) in the context of Fuzzy Data Envelopment Analysis. In our opinion, those that result from using a ranking method to order the fuzzy efficiencies obtained are susceptible to a serious criticism: they are not based on objective criteria. Cross-efficiency evaluation was introduced as an extension of DEA aimed at ranking the DMUs. This methodology has found a significant number of applications and has been extensively investigated. In this chapter, we discuss some difficulties that arise with the definition of fuzzy cross-efficiencies and we propose a fuzzy cross-efficiency evaluation based on the FDE…
A multi-sphere particle numerical model for non-invasive investigations of neuronal human brain activity
2013
In this paper, a multi-sphere particle method is built- up in order to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain activity. The partial difierential equations governing the relationships between neural current sources and the data produced by neuroimaging technique, are able to compute the scalp potential and magnetic fleld distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the computation by avoiding the mesh construction. The current dipoles are into an homogeneous spherical domain modeling the head and the computational approach i…