49,511 research outputs found
Shape optimisation for a class of semilinear variational inequalities with applications to damage models
The present contribution investigates shape optimisation problems for a class
of semilinear elliptic variational inequalities with Neumann boundary
conditions. Sensitivity estimates and material derivatives are firstly derived
in an abstract operator setting where the operators are defined on polyhedral
subsets of reflexive Banach spaces. The results are then refined for
variational inequalities arising from minimisation problems for certain convex
energy functionals considered over upper obstacle sets in . One
particularity is that we allow for dynamic obstacle functions which may arise
from another optimisation problems. We prove a strong convergence property for
the material derivative and establish state-shape derivatives under regularity
assumptions. Finally, as a concrete application from continuum mechanics, we
show how the dynamic obstacle case can be used to treat shape optimisation
problems for time-discretised brittle damage models for elastic solids. We
derive a necessary optimality system for optimal shapes whose state variables
approximate desired damage patterns and/or displacement fields
More Lessons from Taking an AK Model to the Data.
We take an AK model to the PWT data. In the model both technology (intratemporal) and investment (intertemporal) shocks determine the variation of the growth rate. In earlier work we looked at singular models where we extracted only the technology shock using the policy functions from dynamic optimality. Here we recover time series for both shocks for a panel of countries and we isolate what we believe are pervasive patterns in macroeconomic models and postwar data: a negative correlation between intra and intertemporal shocks, and a somewhat lesser role for the intertemporal shock.endogenous growth; technology shocks; investment shocks
Optimality Principles for Model-Based Prediction of Human Gait
Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient\u27s gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait
Computing (R, S) policies with correlated demand
This paper considers the single-item single-stocking non-stationary
stochastic lot-sizing problem under correlated demand. By operating under a
nonstationary (R, S) policy, in which R denote the reorder period and S the
associated order-up-to-level, we introduce a mixed integer linear programming
(MILP) model which can be easily implemented by using off-theshelf optimisation
software. Our modelling strategy can tackle a wide range of time-seriesbased
demand processes, such as autoregressive (AR), moving average(MA),
autoregressive moving average(ARMA), and autoregressive with autoregressive
conditional heteroskedasticity process(AR-ARCH). In an extensive computational
study, we compare the performance of our model against the optimal policy
obtained via stochastic dynamic programming. Our results demonstrate that the
optimality gap of our approach averages 2.28% and that computational
performance is good
Non-stationary Stochastic Optimization
We consider a non-stationary variant of a sequential stochastic optimization
problem, in which the underlying cost functions may change along the horizon.
We propose a measure, termed variation budget, that controls the extent of said
change, and study how restrictions on this budget impact achievable
performance. We identify sharp conditions under which it is possible to achieve
long-run-average optimality and more refined performance measures such as rate
optimality that fully characterize the complexity of such problems. In doing
so, we also establish a strong connection between two rather disparate strands
of literature: adversarial online convex optimization; and the more traditional
stochastic approximation paradigm (couched in a non-stationary setting). This
connection is the key to deriving well performing policies in the latter, by
leveraging structure of optimal policies in the former. Finally, tight bounds
on the minimax regret allow us to quantify the "price of non-stationarity,"
which mathematically captures the added complexity embedded in a temporally
changing environment versus a stationary one
Hierarchical Radio Resource Optimization for Heterogeneous Networks with Enhanced Inter-cell Interference Coordination (eICIC)
Interference is a major performance bottleneck in Heterogeneous Network
(HetNet) due to its multi-tier topological structure. We propose almost blank
resource block (ABRB) for interference control in HetNet. When an ABRB is
scheduled in a macro BS, a resource block (RB) with blank payload is
transmitted and this eliminates the interference from this macro BS to the pico
BSs. We study a two timescale hierarchical radio resource management (RRM)
scheme for HetNet with dynamic ABRB control. The long term controls, such as
dynamic ABRB, are adaptive to the large scale fading at a RRM server for
co-Tier and cross-Tier interference control. The short term control (user
scheduling) is adaptive to the local channel state information within each BS
to exploit the multi-user diversity. The two timescale optimization problem is
challenging due to the exponentially large solution space. We exploit the
sparsity in the interference graph of the HetNet topology and derive structural
properties for the optimal ABRB control. Based on that, we propose a two
timescale alternative optimization solution for the user scheduling and ABRB
control. The solution has low complexity and is asymptotically optimal at high
SNR. Simulations show that the proposed solution has significant gain over
various baselines.Comment: 14 pages, 8 figure
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