810 research outputs found

    An interior-point method for mpecs based on strictly feasible relaxations.

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    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

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    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.

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    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.

    Cellular O-Glycome Reporter/Amplification to explore O-glycans of living cells

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    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

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    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?

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    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 (journal info added
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