a algorithm for convex minimization for convex minimization we introduce an algorithm based on space decomposition the method uses a bundle subroutine to generate a sequence of approximate proximal points when a primal dual track leading to a solution and zero subgradient pair exists these points approximate the primal track points and give the algorithm s or corrector steps the subroutine also approximates dual track points that are gradients needed for the method s newton predictor steps with the inclusion of a simple line search the resulting algorithm is proved to be globally convergent the convergence is superlinear if the primal dual track points and the objective s hessian are approximated well enough

on finite subgroups of su 2 simple lie algebras and the mckay correspondence the question is considered of how the restriction n where n is irreducible for all n and is a finite subgroup of su 2 decomposes into irreducibles for any arbitrary n unk it is announced that using the mckay correspondence the problem has an elegant solution in terms of the coxeter element for the associated lie algebra and that the numbers involved come in a beautiful way from the root structure

active sets nonsmoothness and sensitivity nonsmoothness pervades optimization but the way it typically arises is highly structured nonsmooth behavior of an objective function is usually associated locally with an active manifold on this manifold the function is smooth whereas in normal directions it is vee shaped active set ideas in optimization depend heavily on this structure important examples of such functions include the pointwise maximum of some smooth functions and the maximum eigenvalue of a parametrized symmetric matrix among possible foundations for practical nonsmooth optimization this broad class of partly smooth functions seems a promising candidate enjoying a powerful calculus and sensitivity theory in particular we show under a natural regularity condition that critical points of partly smooth functions are stable small perturbations to the function cause small movements of the critical point on the active manifold

on mathcalvu theory for functions with primal dual gradient structure we consider a general class of convex functions having what we call primal dual gradient structure it includes finitely determined max functions and maximum eigenvalue functions as well as other infinitely defined max functions for a function in this class we discuss a space decomposition that allows us to identify a subspace on which the function appears to be smooth moreover using the special structure of such a function we compute smooth trajectories along which certain second order expansions can be obtained we also give an explicit expression for the hessian of a related lagrangian

practical aspects of the moreau yosida regularization theoretical preliminaries when computing the infimal convolution of a convex function f with the squared norm the so called moreau yosida regularization of f is obtained among other things this function has a lipschitzian gradient we investigate some more of its properties relevant for optimization the most important part of our study concerns second order differentiability existence of a second order development of f implies that its regularization has a hessian for the converse we disclose the importance of the decomposition of bbb r n along cal u the subspace where f is smooth and cal v the subspace parallel to the subdifferential of f

a filled function method for minimizing control variation in constrained discrete time optimal control problems abstract this paper considers a discrete time optimal control problem subject to terminal state constraints and all time step inequality constraints where the cost function involves a terminal cost a summation cost and a penalty on the change of the control action the variation of the control signal and the all time step constraints are non smooth functions thus this optimal control problem is formulated as a non smooth constrained optimization problem however it is nonconvex and hence it may have many local minimum points thus a filled function method is introduced in conjunction with local optimization techniques to solve this non smooth and nonconvex constrained optimization problem for illustration two numerical examples are presented and solved using the proposed approach

identifiable surfaces in constrained optimization the concept of a class c p identifiable surface of a convex set in euclidean space is introduced the paper shows how the smoothness of these surfaces is related to the smoothness of the projection operator and presents finite identification results for certain algorithms for minimization of a function over this set the work uses a partially geometric view of constrained optimization to generalize previous finite identification results

an approximate decomposition algorithm for convex minimization for nonsmooth convex optimization robert mifflin and claudia sagastizabal introduce a vu space decomposition algorithm in mifflin and sagastizabal 2005 11 an attractive property of this algorithm is that if a primal dual track exists this algorithm uses a bundle subroutine with the inclusion of a simple line search it is proved to be globally and superlinearly convergent however a drawback is that it needs the exact subgradients of the objective function which is expensive to compute in this paper an approximate decomposition algorithm based on proximal bundle type method is introduced that is capable to deal with approximate subgradients it is shown that the sequence of iterates generated by the resulting algorithm converges to the optimal solutions of the problem numerical tests emphasize the theoretical findings

cohomology of q convex spaces in top degrees it is shown that every strongly q complete subvariety of a complex analytic space has a fundamental system of strongly q complete neighborhoods as a consequence we find a simple proof of ohsawa s result that every non compact irreducible n dimensional analytic space is strongly n complete finally it is shown that l cohomology theory readily implies ohsawa s hodge decomposition and lefschetz isomorphism theorems for absolutely q convex manifolds

sur la l 2 cohomologie des varietes a courbure negative we give a topological interpretation of the space of l2 harmonic forms on finite volume manifolds with sufficiently pinched negative curvature we give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants the method consists first in comparing l2 cohomology with weighted l2 cohomology thanks to previuos works done by t ohsawa and then in identifying these weighted spaces

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

coincidence point theorems on metric spaces via simulation functions due to its possible applications fixed point theory has become one of the most useful branches of nonlinear analysis in a very recent paper khojasteh et al introduced the notion of simulation function in order to express different contractivity conditions in a unified way and they obtained some fixed point results in this paper we slightly modify their notion of simulation function and we investigate the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions

an approximate u lagrangian and algorithm to uv decomposition in this paper an concept and some properties of approximate u lagrangian are presented they can be reviewed as an extension to the ones of u lagrangian an algorithm for solving an unconstrained minimization problem and the convergence analysis are given when the uv decomposition exists