810 research outputs found
An interior-point method for mpecs based on strictly feasible relaxations.
An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fast-local convergence properties of the algorithm
Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework
We present a new framework for the solution of mathematical programs with
equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is
viewed as a concentration of an unconstrained optimization which minimizes the
complementarity measure and a nonlinear programming with general constraints. A
strategy generalizing ideas of Byrd-Omojokun's trust region method is used to
compute steps. By penalizing the tangential constraints into the objective
function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like
strategy is used to balance the improvements on feasibility and optimality. We
show that, under MPEC-MFCQ, if the algorithm does not terminate in finite
steps, then at least one accumulation point of the iterates sequence is an
S-stationary point
AN INTERIOR-POINT METHOD FOR MPECs BASED ON STRICTLY FEASIBLE RELAXATIONS.
An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fast-local convergence properties of the algorithm.
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Using EPECs to model bilevel games in restructured electricity markets with locational prices
CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context
Cellular O-Glycome Reporter/Amplification to explore O-glycans of living cells
Protein O-glycosylation has key roles in many biological processes, but the repertoire of O-glycans synthesized by cells is difficult to determine. Here we describe an approach termed Cellular O-Glycome Reporter/Amplification (CORA), a sensitive method used to amplify and profile mucin-type O-glycans synthesized by living cells. Cells convert added peracetylated benzyl-α-N-acetylgalactosamine to a large variety of modified O-glycan derivatives that are secreted from cells, allowing for easy purification for analysis by HPLC and mass spectrometry (MS). Relative to conventional O-glycan analyses, CORA resulted in an ∼100-1,000-fold increase in sensitivity and identified a more complex repertoire of O-glycans in more than a dozen cell types from Homo sapiens and Mus musculus. Furthermore, when coupled with computational modeling, CORA can be used for predictions about the diversity of the human O-glycome and offers new opportunities to identify novel glycan biomarkers for human diseases
Optimal control of Allen-Cahn systems
Optimization problems governed by Allen-Cahn systems including elastic
effects are formulated and first-order necessary optimality conditions are
presented. Smooth as well as obstacle potentials are considered, where the
latter leads to an MPEC. Numerically, for smooth potential the problem is
solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an
obstacle potential first numerical results are presented
Apollo asteroids (1566) Icarus and 2007 MK6: Icarus family members?
Although it is more complicated to search for near-Earth object (NEO)
families than main belt asteroid (MBA) families, since differential orbital
evolution within a NEO family can cause current orbital elements to drastically
differ from each other, we have found that Apollo asteroids (1566) Icarus and
the newly discovered 2007 MK6 are almost certainly related. Specifically, their
orbital evolutions show a similar profile, time shifted by only ~1000 yr, based
on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6
along with a possible dust band, the Taurid-Perseid meteor swarm, implies the
first detection of an asteroidal NEO family, namely the "Icarus asteroid
family".Comment: 11 pages, 1 figure, to appear on Astrophysical Journal Letters
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