curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

primal dual interior point methods for semidefinite programming convergence rates stability and numerical results primal dual interior point path following methods for semidefinite programming are considered several variants are discussed based on newton s method applied to three equations primal feasibility dual feasibility and some form of centering condition the focus is on three such algorithms called the xz xz zx and q methods for the xz zx and q algorithms the newton system is well defined and its jacobian is nonsingular at the solution under nondegeneracy assumptions the associated schur complement matrix has an unbounded condition number on the central path under the nondegeneracy assumptions and an additional rank assumption practical aspects are discussed including mehrotra predictor corrector variants and issues of numerical stability compared to the other methods considered the xz zx method is more robust with respect to its ability to step close to the boundary converges more rapidly and achieves higher accuracy

nonlinear semidefinite programming sensitivity convergence and an application in passive reduced order modeling we consider the solution of nonlinear programs with nonlinear semidefiniteness constraints the need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more complicated than the solution of standard nonlinear programs this paper studies a sequential semidefinite programming ssp method which is a generalization of the well known sequential quadratic programming method for standard nonlinear programs we present a sensitivity result for nonlinear semidefinite programs and then based on this result we give a self contained proof of local quadratic convergence of the ssp method we also describe a class of nonlinear semidefinite programs that arise in passive reduced order modeling and we report results of some numerical experiments with the ssp method applied to problems in that class

on stability and the convergence of the kahler ricci flow assuming uniform bounds for the curvature the exponential convergence of the kahler ricci flow is established under two con ditions which are a form of stability the mabuchi energy is bound ed from below and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit

a global algorithm for nonlinear semidefinite programming in this paper we propose a global algorithm for solving nonlinear semidefinite programming problems this algorithm inspired by the classic sqp sequentially quadratic programming method modifies the s sdp sequentially semidefinite programming local method by using a nondifferentiable merit function combined with a line search strategy

a stability instability boundary for disturbance free slow adaptation with unmodeled dynamics the instability of adaptive schemes for small values of parameter adjustment gain has the form of a slow drift of adjustable parameters with an averaging analysis we derive not only a sufficient condition for stability of this drift but also a sufficient condition for it to be unstable a sharp boundary between stability and instability is signal dependent and much less demanding than the usual strict positive realness property the new positivity condition has a simple signal energy interpretation

superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming this paper establishes the superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming sdp under the assumptions that the semidefinite program has a strictly complementary primal dual optimal solution and that the size of the central path neighborhood tends to zero the interior point algorithm considered here closely resembles the mizuno todd ye predictor corrector method for linear programming which is known to be quadratically convergent it is shown that when the iterates are well centered the duality gap is reduced superlinearly after each predictor step indeed if each predictor step is succeeded by r consecutive corrector steps then the predictor reduces the duality gap superlinearly with order 2 1 2 r the proof relies on a careful analysis of the central path for sdp it is shown that under the strict complementarity assumption the primal dual central path converges to the analytic center of the primal dual optimal solution set and the distance from any point on the central path to this analytic center is bounded by the duality gap

stability of slow adaptation for non spr systems with disturbances sufficient conditions are given for the existence of a bounded uniformly asymptotically stable u a s solution of the model reference adaptive control system these conditions which do not require any matching assumptions or knowledge of the order of the plant provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u a s property of the solution is preserved

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

non negative pinching moduli spaces and bundles with infinitely many souls we show that in each dimension n 10 there exist infinite sequences of homotopy equivalent but mutually non homeomorphic closed simply connected riemannian n manifolds with 0 sec 1 positive ricci curvature and uniformly bounded diameter we also construct open manifolds of fixed diffeomorphism type which admit infinitely many complete nonnegatively pinched metrics with souls of bounded diameter such that the souls are mutually non homeomorphic finally we construct examples of noncompact manifolds whose moduli spaces of complete metrics with sec 0 have infinitely many connected components

the rate of convergence of the augmented lagrangian method for nonlinear semidefinite programming we analyze the rate of local convergence of the augmented lagrangian method in nonlinear semidefinite optimization the presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices an implicit function theorem for semismooth functions and variational analysis on the projection operator in the symmetric matrix space without requiring strict complementarity we prove that under the constraint nondegeneracy condition and the strong second order sufficient condition the rate of convergence is linear and the ratio constant is proportional to 1 c where c is the penalty parameter that exceeds a threshold overline c 0

a multivariable self tuning controller based on pole placement design abstract the design problem of controller for discrete time linear multi input output systems is discussed the basic idea is to use pole placement approach a new pole placement tracking problem formulation and its solution is given the design of controller requires no a priori information either about stability or minimum phase of controlled plants the designed controller consists of a feedback part a feedforward part and a new precompensator and is suitable for self tuning control of continuous systems with differing and unknown dead times in each path the controller can have integral action the number of outputs can be different from the number of inputs of the controlled system a reference vector sequence and an effect of the initial state on the system output are given as a left matrix fraction the self tuning algorithm is based on identification of explicit plant model the self tuning algorithm is illustrated by examples

first and second order analysis of nonlinear semidefinite programs in this paper we study nonlinear semidefinite programming problems convexity duality and first order optimality conditions for such problems are presented a second order analysis is also given second order necessary and sufficient optimality conditions are derived finally sensitivity analysis of such programs is discussed

primal dual path following algorithms for semidefinite programming this paper deals with a class of primal dual interior point algorithms for semidefinite programming sdp which was recently introduced by kojima shindoh and hara siam j optim 7 1997 pp 86 125 these authors proposed a family of primal dual search directions that generalizes the one used in algorithms for linear programming based on the scaling matrix x1 2s 1 2 they study three primal dual algorithms based on this family of search directions a short step path following method a feasible potential reduction method and an infeasible potential reduction method however they were not able to provide an algorithm which generalizes the long step path following algorithm introduced by kojima mizuno and yoshise progress in mathematical programming interior point and related methods n megiddor ed springer verlag berlin new york 1989 pp 29 47 in this paper we characterize two search directions within their family as being unique solutions of systems of linear equations in symmetric variables based on this characterization we present a simplified polynomial convergence proof for one of their short step path following algorithms and for the first time a polynomially convergent long step path following algorithm for sdp which requires an extra sqrt n factor in its iteration complexity order as compared to its linear programming counterpart where n is the number of rows or columns of the matrices involved

on the nesterov todd direction in semidefinite programming we study different choices of search direction for primal dual interior point methods for semidefinite programming problems one particular choice we consider comes from a specialization of a class of algorithms developed by nesterov and todd for certain convex programming problems we discuss how the search directions for the nesterov todd nt method can be computed efficiently and demonstrate how they can be viewed as newton directions this last observation also leads to convenient computation of accelerated steps using the mehrotra predictor corrector approach in the nt framework we also provide an analytical and numerical comparison of several methods using different search directions and suggest that the method using the nt direction is more robust than alternative methods

finite settling time stabilisation for multivariable discrete time systems a polynomial equation approach the multivariable case of finite settling time stabilisation fsts of linear discrete time systems is considered in this paper an algebraic approach is adopted which leads to the solution of a polynomial matrix diophantine equation this gives rise to the parametrisation of all fsts controllers in a kucera youla bonjiorno sense and the fsts problem is further reduced to a linear algebra problem over the real numbers subsequently the family of all causal fsts controllers is parametrised and necessary and sufficient conditions for strong fsts stable controllers are derived the minimal mcmillan degree solution and minimal complexity controllers are examined and new bounds are given the analysis provides the means for the parametrisation of families of fsts controllers with certain complexity finally the problems of tracking disturbance rejection and partially assigned dynamics in fst sense are considered and conditions for their solvability are given

deadbeat control of linear discrete time systems by periodic output feedback two deadbeat control problems for open loop time invariant linear discrete time multivariable systems by periodic output feedbacks are formulated and solved sufficient conditions for the existence of solutions to the problems are established procedures for finding solutions to the problems are presented and illustrated by numerical examples

quantitative geometry rather than describing a traditional field of mathematics quantitative geometry refers to a modern way of thinking about geometry and its applications that occur in a wide range of mathematical disciplines the overarching theme here is that certain geometric problems can only be formulated after the introduction of auxiliary quantitative parameters and asking for their asymptotic or approximate behavior this leads to meaningful questions that do not necessarily have counterparts in classical qualitative geometric investigations a viewpoint that allows one to uncover deep and useful structural information that appears only in the quantitative regime quantitative reasoning allows one to tame complicated objects and phenomena that are unwieldy if one insists on exact measurements it is often the case that a rich yet structured picture emerges only if one asks the correct questions by allowing for controlled errors

h optimization and optimal rejection of persistent disturbances abstract in this note it is shown that in a certain well known normed space of persistent signals a natural optimal disturbance rejection problem is equivalent to h optimization thus clarifying certain misconceptions on h optimization in the literature these conclusions are further strengthened using techniques of wiener s generalized harmonic analysis

robust control via sequential semidefinite programming this paper discusses nonlinear optimization techniques in robust control synthesis with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality lmi constraints in tandem with nonlinear matrix equality constraints the latter type of constraints renders the design numerically and algorithmically difficult we solve the optimization problem via sequential semidefinite programming ssdp a technique which expands on sequential quadratic programming sqp known in nonlinear optimization global and fast local convergence properties of ssdp are similar to those of sqp and ssdp is conveniently implemented with available semidefinite programming sdp solvers using two test examples we compare ssdp to the augmented lagrangian method another classical scheme in nonlinear optimization and to an approach using concave optimization

scalar curvature estimates by parallel alternating torsion we generalize llarull s scalar curvature comparison to riemann ian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on 2 tm as a by product we show that the euler number and signature of such manifolds are determined by their global holonomy representation our result holds in particular for all quotients of compact lie groups of equal rank equipped with a normal homogeneous metric we also correct a mistake in the treatment of odd dimensional spaces in our earlier papers

a cheeger finiteness theorem for finsler manifolds abstract in this paper we establish a cheeger finiteness theorem for berwald manifolds moreover a cheeger type estimate on injectivity radii for finsler manifolds is obtained and the existence of the center of mass of a berwald manifold is proved

optimality conditions and global convergence for nonlinear semidefinite programming sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization in this paper we extend theses concepts for nonlinear semidefinite programming we define two sequential optimality conditions for nonlinear semidefinite programming the first is a natural extension of the so called approximate karush kuhn tucker akkt well known in nonlinear optimization the second one called trace akkt is more natural in the context of semidefinite programming as the computation of eigenvalues is avoided we propose an augmented lagrangian algorithm that generates these types of sequences and new constraint qualifications are proposed weaker than previously considered ones which are sufficient for the global convergence of the algorithm to a stationary point

secure key rate of the bb84 protocol using finite sample bits we improve the non asymptotic key rate shown by scarani and renner by proposing several methods to construct tighter conservative confidence intervals of the phase error rate than one previously shown in addition we show that the accurate channel estimation method non asymptotically increases the key rate over the amplitude damping channel as well as the asymptotic case in the bb84 protocol

local and superlinear convergence of a primal dual interior point method for nonlinear semidefinite programming in this paper we consider a primal dual interior point method for solving nonlinear semidefinite programming problems we propose primal dual interior point methods based on the unscaled and scaled newton methods which correspond to the aho hrvw ksh m and nt search directions in linear sdp problems we analyze local behavior of our proposed methods and show their local and superlinear convergence properties

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

ripple free tracking problem in the deadbeat control of discrete plants originating from continuous ones it is important to have exact tracking not only at the sampling instants but also in between the instants this paper investigates such a problem in the general case of a reference signal that can vary within a pre specified class the design procedure proposed here is based on a polynomial algebra approach an internally stable closed loop system is derived by means of an algorithm where the transfer function of the controller originates from the solution of a set of linear equations algebraic conditions are given to determine the minimum time control scheme numerical examples are reported to show the feasibility of the method and the simplicity of including other specific requirements into the control law

interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices the sdlcp semidefinite linear complementarity problem in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization it is defined as the problem of finding a pair x y of n times n symmetric positive semidefinite matrices which lies in a given n n 1 2 dimensional affine subspace fc of sc 2 and satisfies the complementarity condition x bullet y 0 where sc denotes the n n 1 2 dimensional linear space of symmetric matrices and x bullet y the inner product of x and y the problem enjoys a close analogy with the lcp in the euclidean space in particular the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace fc the aim of this paper is to establish a theoretical basis of interior point methods with the use of newton directions toward the central trajectory for the monotone sdlcp

ricci curvature bounds and einstein metrics on compact manifolds where f mo m1 is a homeomorphism and dil f is the dilatation of f given by dil f supx x2 dist f x f x2 dist x1 x2 if mo and m1 are not homeomorphic define dl mo mi oo gromov 20 proves the remarkable result that the space of compact riemannian manifolds f a 3 d of sectional curvature iki 3 0 and diameter dm v and diameter dm c iki dm vm1 in particular gromov s compactness theorem may be strengthened to the statement that f a v d is c1 l compact in the lipschitz topology in this paper we study the question of lipschitz convergence of compact riemannian manifolds with bounds imposed on the ricci curvature ric in

simplicial matrix tree theorems first published in transactions of the american mathematical society in volume 361 2009 no 11 6073 6114 published by the american mathematical society

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

two sided equations and skew primeness for n d polynomial matrices abstract the two sided equations in n d polynomial matrices are studied which are often encountered in control problems the solvability conditions are derived the general and minimum degree solutions are investigated and two algorithms of solution are proposed the related concept of skew primeness is generalized for n d polynomials

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

a state space solution of bilateral diophantine equations over rh abstract this paper studies a class of real rational matrix bilateral diophantine equations bde arising in numerous control problems a necessary and sufficient solvability condition is derived in terms of state space realizations of rational matrices involved in the equation this condition is given in terms of a constrained matrix sylvester equation and is numerically tractable an explicit state space parametrization of all solutions is also derived this parameterization effectively includes two parameters one is a standard rh parameter and another one arises if the sylvester equation is non uniquely solvable a condition in terms of zeros of rational matrices involved in the bde is found under which the sylvester equation has a unique solution and hence the parametrization is affine in a single rh parameter

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

deadbeat servoproblem for multivariable n d systems sufficient conditions are given for the existence of a solution to the deadbeat servoproblem for multivariable n d linear systems an algorithm is presented for finding matrices of an n d linear controller the algorithm is illustrated by a simple example

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

ripple free robust output regulation and tracking for multirate sampled data control the problem of the robust continuous time asymptotic tracking and disturbance rejection for a multivariable multirate sampled data system is studied the necessity of a continuous time internal model of the exogenous signals except for the constant ones if any for obtaining a ripple free zero error response is proven the conditions are given for the existence of a hybrid control system including possibly a continuous time subcompensator for which the exponential stability and a continuous time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters this in particular both for when the dead beat convergence of the state free response and the continuous time error response is required at the nominal parameters and for when an exponential convergence with a prescribed rate of decay is required including design procedures of the continuous time and the discrete time subcompensators both for when the available description of the plant has a

smooth approximation of lipschitz functions on riemannian manifolds abstract we show that for every lipschitz function f defined on a separable riemannian manifold m possibly of infinite dimension for every continuous e m 0 and for every positive number r 0 there exists a c smooth lipschitz function g m r such that f p g p e p for every p m and lip g lip f r consequently every separable riemannian manifold is uniformly bumpable we also present some applications of this result such as a general version for separable riemannian manifolds of deville godefroy zizler s smooth variational principle

an augmented lagrangian method for a class of lmi constrained problems in robust control theory we present a new approach to a class of non convex lmi constrained problems in robust control theory the problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality lmi constraints in tandem with non convex constraints related to rank deficiency conditions we solve these problems using an extension of the augmented lagrangian technique the lagrangian function combines a multiplier term and a penalty term governing the non convex constraints the lmi constraints due to their special structure are retained explicitly and not included in the lagrangian global and fast local convergence of our approach is then obtained either by an lmi constrained newton type method including line search or by a trust region strategy the method is conveniently implemented with available semi definite programming sdp interior point solvers we compare its performance to the wellknown d k iteration scheme in robust control two test problems are investigated and

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a strategy of global convergence for the affine scaling algorithm for convex semidefinite programming the affine scaling algorithm is one of the earliest interior point methods developed for linear programming this algorithm is simple and elegant in terms of its geometric interpretation but it is notoriously difficult to prove its convergence it often requires additional restrictive conditions such as nondegeneracy specific initial solutions and or small step length to guarantee its global convergence this situation is made worse when it comes to applying the affine scaling idea to the solution of semidefinite optimization problems or more general convex optimization problems in math program 83 1 3 393 406 1998 muramatsu presented an example of linear semidefinite programming for which the affine scaling algorithm with either short or long step converges to a non optimal point this paper aims at developing a strategy that guarantees the global convergence for the affine scaling algorithm in the context of linearly constrained convex semidefinite optimization in a least restrictive manner we propose a new rule of step size which is similar to the armijo rule and prove that such an affine scaling algorithm is globally convergent in the sense that each accumulation point of the sequence generated by the algorithm is an optimal solution as long as the optimal solution set is nonempty and bounded the algorithm is least restrictive in the sense that it allows the problem to be degenerate and it may start from any interior feasible point

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

nonnegative curvature and cobordism type we show that in each dimension n 4k k 2 there exist infinite sequences of closed simply connected riemannian n manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type

quantitative null cobordism author s chambers gregory r dotterrer dominic manin fedor weinberger shmuel abstract for a given null cobordant riemannian n manifold how does the minimal geometric complexity of a null cobordism depend on the geometric complexity of the manifold in gro99 gromov conjectured that this dependence should be linear we show that it is at most a polynomial whose degree depends on n this construction relies on another of independent interest take x and y to be sufficiently nice compact metric spaces such as riemannian manifolds or simplicial complexes suppose y is simply connected and rationally homotopy equivalent to a product of eilenberg maclane spaces for example any simply connected lie group then two homotopic l lipschitz maps f g x rightarrow y are homotopic via a cl lipschitz homotopy we present a counterexample to show that this is not true for larger classes of spaces y

the strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications for a locally optimal solution to the nonlinear semidefinite programming problem under robinson s constraint qualification the following conditions are proved to be equivalent the strong second order sufficient condition and constraint nondegeneracy the nonsingularity of clarke s jacobian of the karush kuhn tucker system the strong regularity of the karush kuhn tucker point and others

a predictor corrector interior point algorithm for the semidefinite linear complementarity problem using the alizadeh haeberly overton search direction this paper proposes a globally convergent predictor corrector infeasible interior point algorithm for the monotone semidefinite linear complementarity problem using the alizadeh haeberly overton search direction and shows its quadratic local convergence under the strict complementarity condition

quantitative algebraic topology and lipschitz homotopy we consider when it is possible to bound the lipschitz constant a priori in a homotopy between lipschitz maps if one wants uniform bounds this is essentially a finiteness condition on homotopy this contrasts strongly with the question of whether one can homotop the maps through lipschitz maps we also give an application to cobordism and discuss analogous isotopy questions

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented

deadbeat characteristic of one step ahead control abstract the deadbeat characteristic of one step ahead control is examined in detail it has been clarified that the plant output y k coincides with the reference output y m k for all k n 1 n m where n is the order of the plant and n m is the relative degree of the plant transfer function