a new completely general class of variational inclusions with noncompact valued mappings abstract in this paper we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms we prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms

algorithm for generalized co complementarity problems in banach spaces abstract in this paper we introduce a new class of generalized co complementarity problems in banach spaces an iterative algorithm for finding approximate solutions of these problems is considered some convergence results for this iterative algorithm are derived and several existence results are obtained

necessary conditions for optimal control problems with state constraints necessary conditions of optimality are derived for optimal control problems with pathwise state constraints in which the dynamic constraint is modelled as a differential inclusion the novel feature of the conditions is the unrestrictive nature of the hypotheses under which these conditions are shown to be valid an euler lagrange type condition is obtained for problems where the multifunction associated with the dynamic constraint has values possibly unbounded nonconvex sets and satisfies a mild one sided lipschitz continuity hypothesis we recover as a special case the sharpest available necessary conditions for state constraint free problems proved in a recent paper by ioffe for problems where the multifunction is convex valued it is shown that the necessary conditions are still valid when the one sided lipschitz hypothesis is replaced by a milder local hypothesis a recent dualization theorem permits us to infer a strengthened form of the hamiltonian inclusion from the euler lagrange condition the necessary conditions for state constrained problems with convex valued multifunctions are derived under hypotheses on the dynamics which are significantly weaker than those invoked by loewen and rockafellar to achieve related necessary conditions for state constrained problems and improve on available results in certain respects even when specialized to the state constraint free case proofs make use of recent decoupling ideas of the authors which reduce the optimization problem to one to which pontryagin s maximum principle is applicable and a refined penalization technique to deal with the dynamic constraint

a maximum principle for nonsmooth optimal control problems with state constraints abstract optimality conditions are derived in the form of a maximum principle governing solutions to an optimal control problem which involves state constraints the conditions which apply in the absence of differentiability assumptions on the data are stated in terms of clarke s generalized jacobians although not the most general available the conditions are derived by a novel method this involves removal of the state constraints by introduction of a penalty term and application of ekeland s variational principle

projection methods isotone projection cones and the complementarity problem one studies some iterative methods for solving complementarity problems explicit or implicit in hilbert spaces the iterative methods presented are based on the fixed point theory on the coincidence equations on convex cones and on some properties of projection operators onto a special cone named the isotone projection cone the ordering defined by the cone is essential for the complementarity theory the idea is to use systematically the ordering in the iterative methods for solving complementarity problems in this sense one shows that the isotone projection cone is a good instrument

a maximum principle for free endtime optimal control problems with data discontinuous in time recently a maximum principle has been proved for free endtime problems when the dynamics and the control constraint set are assumed to be merely measurable with respect to the time variable a new simple derivation of this optimality condition is given from standard fixed endtime results it involves a generalization of the customary boundary condition on the maximized hamiltonian function evaluated along the optimal state trajectory and costate function the hypotheses under which the maximum principle is proved permit unilateral state constraints data merely lipschitz continuous in the state variable and endpoint constraints expressed as general set inclusions the primary concern is with methodology and setting down a simple proof of the maximum principle for problems with data measurable in the time variable

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

algorithm for generalized multivalued variational inequalities in hilbert spaces abstract we introduce a new class of generalized multivalued variational inequality problems 1 1 which contain several existing variational inequality problems as special cases an iterative algorithm for finding approximate solutions of problem 1 1 is considered several convergence results for this algorithm are derived and in particular several existence results of problems 1 1 are obtained we also introduce a new class of generalized multivalued complementarity problems 5 1 which also contain several known complementarity problems as special cases it is shown that problem 5 1 is equivalent to problem 1 1 of special type from which several existence results of problem 5 1 are obtained

a maximum principle for differential inclusion problems with state constraints we study boundary trajectories of differential inclusions with state constraints and prove a maximum principle of the pontryagin type with the adjoint equation and the maximum condition separated we obtain a more general theorem and use a different method of proof than in previous results of this type

iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities in this paper we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include as a special case some known results in this field our results are the extension and improvements of the results of siddiqi and ansari ding and zeng

iterative methods for a class of complementarity problems abstract in this paper we propose and study an algorithm for a new class of complementarity problems of finding u r n such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a nonlinear transformation from r n into itself it is proved that the approximate solution obtained from the iterative scheme converges to the exact solution several special cases are also discussed

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

a connection between the maximum principle and dynamic programming for constrained control problems we consider the mayer optimal control problem with dynamics given by a nonconvex differential inclusion whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function this additional relation is applied in turn to show that the maximum principle is nondegenerate we also provide a sufficient condition for the normality of the maximum break principle to derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories then duality theory of convex analysis is applied to derive necessary conditions for optimality in this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case

adaptive predictor based on maximally flat halfband filter in lifting scheme for complex short time varying signals a high order predictor does not always yield good performance for this we investigate the use of a short order adaptive predictor since the maximally flat filters are the optimal predictors for polynomial signal prediction the adaptation is based on the combination of a set of maximally flat filters for compression efficiency the dynamic ranges of the weighting variables are specially considered for this based on the bernstein filters another form to represent the weighting variables is used these two sets of weighting coefficients can be transformed into each other with a simple linear transform thus the adaptation can be made in both the time domain and the frequency domain for block based image coding the least square criterion is used to derive the weighting coefficients experimental results show that the adaptive predictor performs better than the s p transform the median edge detector med and the gradient adjusted predictor gap

epi lipschitz like sets in banach space theorems and examples on considere un espace de banach x et on etudie quelles proprietes un ensemble c dans x doit avoir pour que le cone tangent de clarke t c x et le cone normal n c x mesurent adequatement le comportement a la frontiere de x dans c

the quasi complementarity problem abstract variational inequality techniques are used to suggest a unified and general iterative algorithm for computing the approximate solution of a new class of complementarity problems the convergence properties of this algorithm are also discussed

image coding using adaptive recursive interpolative dpcm a predictive image coder having minimal decoder complexity is presented the image coder utilizes recursive interpolative dpcm in conjunction with adaptive classification entropy constrained trellis coded quantization and optimal rate allocation to obtain signal to noise ratios snrs in the range of those provided by the most advanced transform coders

semistability of nonlinear systems having a connected set of equilibria and time delays in this technical note we develop a semistability analysis framework for nonlinear systems with bounded time varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown heterogeneous time varying delays along the communication links we show that for such a nonlinear system having nonisolated equilibria if the system asymptotically converges to a constant time delay system and this new system is semistable then the original time varying delay system is semistable in proving our results we extend the limiting differential equation approach to time varying delay systems and also develop some new convergence results for functional differential equations

random generalized nonlinear variational inclusions for random fuzzy mappings in this paper we introduce and study a new class of random set valued nonlinear generalized variational inclusions with noncompact valued random fuzzy mappings and construct a new iterative algorithm we also discuss the existence of random solutions for this class of random fuzzy variational inclusions and the convergence of random iterative sequences generated by the algorithm

an integral type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints abstract for optimal control problems involving ordinary differential equations and functional inequality state constraints the maximum principle may degenerate producing no useful information about minimizers this is known as the degeneracy phenomenon several non degenerate forms of the maximum principle valid under different constraint qualifications have been proposed in the literature in this paper we propose a new constraint qualification under which a nondegenerate maximum principle is validated in contrast with existing results our constraint qualification is of an integral type an advantage of the proposed constraint qualification is that it is verified on a larger class of problems with nonsmooth data and convex velocity sets

on the nonlinear complementarity problem abstract we consider and study an algorithm for a new class of complementarity problems of finding u such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a diagonally nonlinear mapping from r n into itself furthermore it is proved that the approximate solution obtained by the iterative scheme converges to the exact solution special cases are also discussed

generalized nonlinear mixed quasi variational inequalities abstract in this paper we introduce and study a new class of quasi variational inequalities which is called the generalized nonlinear set valued mixed quasi variational inequality using the resolvent operator technique for maximal monotone mapping we construct some new iterative algorithms for solving this class of generalized nonlinear set valued mixed quasi variational inequalities we prove the existence of solution for this kind of generalized nonlinear set valued mixed quasivariational inequalities without compactness and the convergence of iterative sequences generated by the algorithms we also discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear mixed quasi variational inequalities

on multivalued complementarity problems in banach spaces in this paper we prove a new existence result for multivalued complementarity problems in banach spaces our result represents a refinement and improvement of the previously known results

mann and ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi variational inclusions abstract in this paper we introduce a new class of generalized nonlinear implicit quasi variational inclusions and prove its equivalence with a class of fixed point problems by making use of the properties of maximal monotone we also prove the existence of solutions for this generalized nonlinear implicit quasi variational inclusions and the convergence of iterative sequences generated by the perturbed algorithms

measure driven differential inclusions measure driven differential inclusions arise when we attempt to derive necessary conditions of optimality for optimal impulsive control problems with nonsmooth data we introduce the concept of a robust solution to a measure driven inclusion which extends to a multifunction setting interpretations of solutions to measure driven differential equations provided by dal maso and rampazzo and others closure properties of sets of robust solutions are established and notions of relaxation investigated implications for optimality conditions for impulsive control problems are pursued in a companion paper

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities