dirichlet problem for demi coercive functionals on considere des fonctionnelles integrales du type f u f du ou f r n 0 est une fonction convexe ayant la propriete suivante il existe a 0 b 0 r n tel que f z a z b z r n

compatibility conditions for nonlinear neumann problems abstract results we recall an abstract definition introduced in the general framework of the minimization of non coercive functionals see bbgt definition 2 1 let v a be a topological vector space and let f v co co be any mapping we call a sequential recession functional the mapping f u inf lim inf i f tnun t al u p u n m t i where t and u are sequences notice that when f is convex and a lower semicontinuous f coincides with the usual recession functional see for instance r f tu u f v lim t r r to2 where u is any point in dom f in the following we set ker f u e i f u o remark that in general ker f is not a subspace but is a possibly nonconvex set of half lines starting from the origin the following necessary condition for existence was proved in bbgt proposition 2 2 assume that the problem min f u ue v 2 1

on the topology and index of minimal surfaces we show that for an immersed two sided minimal surface in r 3 there is a lower bound on the index depending on the genus and number of ends using this we show the nonexistence of an embedded minimal surface in r 3 of index 2 as conjectured by choe cho90 moreover we show that the index of an immersed two sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface

noncoercive variational inequalities some applications ever since the fundamental paper of lions and stampacchia io the subject of variational inequalities has become a very active area of study and become an important tool in the study of nonlinear partial differential equations which are subject to various types of constraints see e g l 5 8 111 in lo the authors consider first the case of coercive forms and then using elliptic regularization problems involving noncoercive but nonnegative forms we shall use a similar approach to study variational inequalities involving noncoercive bilinear forms and nonlinear functionals which are nice perturbations of lower semi continuous convex functionals furthermore our bilinear forms need not necessarily have a finite dimensional kernel our investigation has been motivated by some work of baiocchi gastaldi and tomarelli see 3 61 where variational inequalities involving so called compact coercive bilinear forms are studied we shall introduce here a somewhat more general concept that of a p coercive bilinear form and study variational inequalities involving such forms and nonlinear functionals which are compact and bounded perturbations of lower semi continuous convex functionals in the next section we shall introduce the necessary terminology prove some preliminary results and give the statement of the abstract problem we then shall state and prove our main abstract result and conclude the paper with applications including one to the study of a flat plate on an elastic foundation with unilateral boundary conditions see e g l for the terminology and one to the study of unilateral problems in semipermeable media see 5

one sided complete stable minimal surfaces we prove that there are no complete one sided stable minimal surfaces in the euclidean 3 space we classify least area surfaces in the quotient of mathbb r 3 by one or two linearly independent translations and we give sharp upper bounds of the genus of compact two sided index one minimal surfaces in non negatively curved ambient spaces finally we estimate from below the index of complete minimal surfaces in flat spaces in terms of the topology of the surface

immersions minimales premiere valeur propre du laplacien et volume conforme generalisation de quelques resultats de li yau en toute dimension caracterisation de la metrique admettant des immersions minimales par ses premieres fonctions propres

quantitative index bounds for translators via topology we obtain a quantitative estimate on the generalised index of translators for the mean curvature flow with bounded norm of the second fundamental form the estimate involves the dimension of the space of weighted square integrable f harmonic 1 forms by the adaptation to the weighted setting of li tam theory developed in previous works this yields estimates in terms of the number of ends of the hypersurface when this is contained in a upper halfspace with respect to the translating direction when there exists a point where all principal curvatures are distinct we estimate the nullity of the stability operator this permits to obtain quantitative estimates on the stability index via the topology of translators with bounded norm of the second fundamental form which are either two dimensional or in higher dimension have finite topological type and are contained in a upper halfspace

index one minimal surfaces in spherical space forms abstract we prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two this confirms a conjecture of r schoen for an infinite class of 3 manifolds

min max minimal hypersurface in manifolds with convex boundary and hbox ric ge 0 let m n 1 partial m g be a compact manifold with non negative ricci curvature convex boundary and 2 le n le 6 we show that the min max minimal hypersurface with respect to one parameter families of hypersurfaces in m partial m is orientable of index one and multiplicity one

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

a hybrid immune multiobjective optimization algorithm in this paper we develop a hybrid immune multiobjective optimization algorithm himo based on clonal selection principle in himo a hybrid mutation operator is proposed with the combination of gaussian and polynomial mutations gp hm operator the gp hm operator adopts an adaptive switching parameter to control the mutation process which uses relative large steps in high probability for boundary individuals and less crowded individuals with the generation running the probability to perform relative large steps is reduced gradually by this means the exploratory capabilities are enhanced by keeping a desirable balance between global search and local search so as to accelerate the convergence speed to the true pareto optimal front in the global space with many local pareto optimal fronts when comparing himo with various state of the art multiobjective optimization algorithms developed recently simulation results show that himo performs better evidently

unilateral contact of two solids subject to large deformations formulation and existence results the approach that is currently the most widely used for formulating the unilateral frictionless contact between two deformable solids involves two key elements the orthogonal projection of one potential contact material surface on another and the action reaction principle of contact forces in the present paper we investigate this approach in the general case of large deformations and study unilateral frictionless boundary value problems of elasticity formulated by means of it the conditions for the orthogonal projection to be unique or further a c 1 diffeomorphism are established an extended action reaction principle is explicitly given for the forces acting on a pair of potential contact surfaces assuming the solids under consideration can be described by polyconvex hyperelastic laws we formulate the associated unilateral frictionless boundary value problem as a minimum principle and show the existence of a solution to it

existence theorems for generalized noncoercive equilibrium problems the quasi convex case we provide a characterization of the nonemptiness of the solution set for generalized noncoercive equilibrium problems an extension of generalized quasi variational inequalities defined in reflexive banach spaces in the quasi convex case in addition several necessary and sufficient conditions for the set of solutions to these problems to be nonempty and bounded are also given our approach is based on recession notions which proved to be very useful in the study of noncoercive minimization problems in fact we find some particular cones as estimates for the recession cone of the solution set these cones for the ones containing the latter set are proved to be sharp enough to encompass several special situations found in the literature

differential evolution with dynamic stochastic selection for constrained optimization how much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper stochastic ranking has been demonstrated as an effective technique for constrained optimization in stochastic ranking the comparison probability will affect the position of feasible solution after ranking and the quality of the final solutions in this paper the dynamic stochastic selection dss is put forward within the framework of multimember differential evolution firstly a simple version named dss mde is given where the comparison probability decreases linearly the algorithm dss mde has been compared with two state of the art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions dss mde is also evaluated on four well studied engineering design examples and the experimental results are significantly better than current available results secondly other dynamic settings of the comparison probability for dss mde are also designed and tested from the experimental results dss mde is effective for constrained optimization finally dss mde with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in cec 06 and the experimental results on most functions are competitive

kernel induced fuzzy clustering of image pixels with an improved differential evolution algorithm a modified differential evolution de algorithm is presented for clustering the pixels of an image in the gray scale intensity space the algorithm requires no prior information about the number of naturally occurring clusters in the image it uses a kernel induced similarity measure instead of the conventional sum of squares distance use of the kernel function makes it possible to partition data that is linearly non separable and non hyper spherical in the original input space into homogeneous groups in a transformed high dimensional feature space a novel search variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices extensive performance comparison over a test suite of 10 gray scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state of the art algorithms for automatic multi class image segmentation

existence of optimal solutions and duality results under weak conditions in this paper we consider an ordinary convex program with no qualification conditions such as slater s condition and for which the optimal set is neither required to be compact nor to be equal to the sum of a compact set and a linear space it is supposed only that the infimum is finite a very wide class of convex functions is exhibited for which the optimum is always attained and is equal to the supremum of the ordinary dual program additional results concerning the existence of optimal solutions in the non convex case are also given

contact between nonlinearly elastic bodies we study the contact between nonlinearly elastic bodies by variational methods after the formulation of the mechanical problem we provide existence results based on polyconvexity and on quasiconvexity then we derive the euler lagrange equation as a necessary condition for minimizers here clarke s generalized gradients are the essential tool to treat the nonsmooth obstacle condition

relaxed formulation and existence result of the degenerated elliptic small disturbance model abstract we consider an elliptic parabolic pde governing the flow of a steady state two dimensional irrotational compressible fluid in a channel or around a thin profile the model is formulated in term of a noncoercive variational problem with an integral functional in a truncated domain we propose a relaxed formulation in the bounded variation functions space and we prove the existence and the uniqueness of the relaxed optimal solution we consider also the asymptotic behavior of the solution when the domain grows to infinity

a new hybrid differential evolution with simulated annealing and self adaptive immune operation differential evolution de has become a very powerful tool for global continuous optimization many strategies have been proposed for the generation of new solutions and every strategy has its own pros and cons so which one of them should be selected is critical for de performance besides being problem dependent in this paper different new solution generation strategies are integrated together and the individual advantages of different generation strategies are utilized to enhance the exploring ability and or to accelerate the convergence simulated annealing idea is introduced to escape from possible local optimum attraction clonal selection operation employs self adaptive gaussian hyper mutation along each dimension to focus the exploitation on the promising areas and exerts different influences on different dimensions experiments show that the proposed ideas benefit the performance of the algorithm and the proposed algorithm performs comprehensively better than other de variants in terms of convergence stability and solution accuracy

a new conformal invariant and its applications to the willmore conjecture and the first eigenvalue of compact surfaces let m be a compact riemannian manifold with a fixed conformal structure then we introduce the concept of conformal volume of m in the following manner for each branched conformal immersion q9 of m into the unit sphere s n we consider the set of all branched conformal immersions obtained by composi t ion of qo with the conformal automorphisms of s we let vc n qg be the max imum volume of these branched immersions the conformal volume of m is defined to be the infimum of v n q0 where qo ranges over all branched conformal immersions of m into the unit sphere s in this paper we study the case when m is a compact surface and we call the conformal volume of m to be the conformal area of m we demonst ra te that this conformal invariant is non trivial in fact we prove that if there exists a minimal immersion of m into s where coordinate functions are first eigenfunctions then the conformal area of m is given by the area of m with respect to the induced metric this enables us to compute the conformal area for several surfaces for example the conformal area of r p z is 6n and the conformal area of the square torus is 27c 2 we believe that the computa t ion of the conformal area for general surfaces will be very impor tant in studying the geometry of compact surfaces we demonstrate this claim by applying the concept of conformal area to two different branches of surface theory the first application is to study the total curvature of a compact surface in r this problem has a long history fenchel and fary 9 proved that for a closed curve o in r slk 27c where k is its curvature then milnor 12

new existence results for equilibrium problems we consider equilibrium problems in the framework of the formulation proposed by blum and oettli which includes variational inequalities nash equilibria in noncooperative games and vector optimization problems for instance as particular cases we establish new sufficient and or necessary conditions for existence of solutions of such problems our results are based upon the relation between equilibrium problems and certain auxiliary convex feasibility problems together with extensions to equilibrium problems of gap functions for variational inequalities then we apply our results to some particular instances of equilibrium problems obtaining results which include among others a new lemma of the alternative for convex optimization problems

on stable compact minimal submanifolds of riemannian product manifolds abstract in this paper we prove a classification theorem for stable compact minimal submanifolds of a riemannian product of an m 1 dimensional m 1 3 hypersurface m 1 in euclidean space and any riemannian manifold m 2 when the sectional curvature k m 1 of m 1 satisfies 1 m 1 1 k m 1 1 in particular when the ambient space is an m dimensional m 3 compact hypersurface m in euclidean space if the sectional curvature k m of m satisfies 1 m 1 k m 1 then we conclude that there exist no stable compact minimal submanifolds in m

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

minimal hypersurfaces with bounded index we prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index and volume if the ambient dimension is greater than three in a riemannian manifold m n g 3 le n le 7 can degenerate loosely speaking our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces up to controlled errors several compactness finiteness theorems follow from our local picture

convex analysis can be helpful for the asymptotic analysis of monotone operators asymptotic analysis of monotone operators we use representations of maximal monotone operators for studying recession or asymptotic operators associated to maximal monotone operators such a concept is useful for dealing with unboundedness

general curvature estimates for stable h surfaces in 3 manifolds applications we obtain an estimate for the norm of the second fundamental form of stable h surfaces in riemannian 3 manifolds with bounded sectional curvature our estimate depends on the distance to the boundary of the surface and on the bound on the sectional curvature but not on the manifold itself we give some applications in particular we obtain an interior gradient estimate for h sections in killing submersions

existence theorems for contact with friction of two linear elastic bodies abstract in this article i give an iteration method for solving the signorini problem by the idea of concentration cancellation the nonlinear quantity in the mathematical formulation of the problem caused by contact friction effect on the boundary is relaxed to a convex functional therefore the relaxed problem can be solved by using convex minimization techniques which are numerically stable finally good convergence property of the proposed method is proved

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

general existence theorems for unilateral problems in continuum mechanics the problem of minimizing a possibly non convex and non coercive functional is studied either necessary or sufficient conditions for the existence of solutions are given involving a generalized recession functional whose properties are discussed thoroughly the abstract results are applied to find existence of equilibrium configurations of a deformable body subject to a system of applied forces and partially constrained to lie inside a possibly unbounded region

estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems economic load dispatch eld is an important and difficult optimization problem in power system planning this article aims at addressing two practically important issues related to eld optimization 1 analyzing the eld problem from the perspective of evolutionary optimization 2 developing effective algorithms for eld problems of large scale the first issue is addressed by investigating the fitness landscape of eld problems with the purpose of estimating the expected performance of different approaches to address the second issue a new algorithm named estimation of distribution and differential evolution cooperation ed de is proposed which is a serial hybrid of two effective evolutionary computation ec techniques estimation of distribution and differential evolution the advantages of ed de over the previous eld optimization algorithms are experimentally testified on eld problems with the number of generators scaling from 10 to 160 the best solution records of classical 13 and 40 generator eld problems with valve points and the best solution records of 10 20 40 80 and 160 generator eld problems with both valve points and multiple fuels are updated in this work to further evaluate the efficiency and effectiveness of ed de we also compare it with other state of the art evolutionary algorithms eas on typical function optimization tasks

index estimates for free boundary minimal hypersurfaces we show that the morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the euclidean space grows linearly with the dimension of its first relative homology group which is at least as big as the number of its boundary components minus one in ambient dimension three this implies a lower bound for the index of a free boundary minimal surface which is linear both with respect to the genus and the number of boundary components thereby the compactness theorem by fraser and li implies a strong compactness theorem for the space of free boundary minimal surfaces with uniformly bounded morse index inside a convex domain our estimates also imply that the examples constructed in the unit ball by fraser schoen and folha pacard zolotareva have arbitrarily large index extensions of our results to more general settings including various classes of positively curved riemannian manifolds and other convexity assumptions are discussed

an effective memetic differential evolution algorithm based on chaotic local search this paper proposes an effective memetic differential evolution de algorithm or decls that utilizes a chaotic local search cls with a shrinking strategy the cls helps to improve the optimizing performance of the canonical de by exploring a huge search space in the early run phase to avoid premature convergence and exploiting a small region in the later run phase to refine the final solutions moreover the parameter settings of the decls are controlled in an adaptive manner to further enhance the search ability to evaluate the effectiveness and efficiency of the proposed decls algorithm we compared it with four state of the art de variants and the ipop cma es algorithm on a set of 20 selected benchmark functions results show that the decls is significantly better than or at least comparable to the other optimizers in terms of convergence performance and solution accuracy besides the decls has also shown certain advantages in solving high dimensional problems

compactness properties for families of quasistationary solutions of some evolution equations the following typical problem occurs in passing to the limit in some phase field models for two sequences of space time dependent functions n x n representing e g suitable approximations of the temperature and the phase variable we know that the sum n x n converges in some l p space as n and that the time integrals of a suitable space functional evaluated on n x n are uniformly bounded with respect to n can we deduce that n and x n converge separately luckhaus 1990 gave a positive answer to this question in the framework of the two phase stefan problem with gibbs thompson law for the melting temperature plotnikov 1993 proposed an abstract result employing the original idea of luckhaus and arguments of compactness and reflexivity type we present a general setting for this and other related problems providing necessary and sufficient conditions for their solvability these conditions rely on general topological and coercivity properties of the functionals and the norms involved and do not require reflexivity

noncoercive optimization problems this paper modifies a recent sufficient condition for the existence of optimal solutions proposed by buttazzo and tomarelli to obtain a condition that is necessary and sufficient applications to mathematical programming are given and stability results established

how to deal with the unbounded in optimization theory and algorithms the aim of this survey is to show how the unbounded arises in optimization problems and how it leads to fundamental notions which are not only useful for proving theoretical results such as convergence of algorithms and the existence of optimal solutions but also for constructing new methods

unilateral problems in nonlinear three dimensional elasticity in 1977 john ball obtained a series of very important existence results in hyperelasticity the objective of the present paper is to extend his results in two directions first by considering unilateral boundary conditions corresponding to contact without friction secondly by allowing locking constraints in the set of admissible deformations