optimality for nonsmooth fractional multiple objective programming abstract in this study the necessary and sufficient optimality conditions for nonsmooth fractional multiple objective optimization problems are provided our idea is based on using the properties of limiting subdifferential vectors in nonsmooth analysis and a separation theorem in convex analysis

multiple objective programs in banach spaces sufficiency for proper optimality abstract this paper establishes some sufficient conditions for optimality and proper optimality for multiple objective programs in banach spaces after extending the concept of vector invexity

minimax programming under p r invexity abstract minimax programming problems involving p r invex functions with respect to are considered parametric and non parametric necessary and sufficient optimality conditions and duality results for a class of minimax programming problems are obtained under p r invexity assumption on objective and constraint functions some different types of dual problems are introduced and duality theorems is established for each dual problem

an ϵ sensitivity analysis for semidefinite programming abstract we extend the concept of sensitivity analysis developed for linear programming to that for semidefinite programming first the notion of optimality for a given semidefinite programming problem is defined and then a generic sensitivity analysis for semidefinite programming is introduced based on the definitions we develop an implementation of the generic sensitivity analysis under perturbations of either the cost parameters or the right hand side

optimality and invexity in optimization problems in banach algebras spaces abstract in this paper we introduce into nonsmooth optimization theory in banach algebras a new class of mathematical programming problems which generalizes the notion of smooth kt p r invexity in fact this paper focuses on the optimality conditions for optimization problems in banach algebras regarding the generalized kt p r invexity notion and kuhn tucker points

a proof for antczak s mean value theorem in invexity analysis abstract this paper provides another proof for antczak s mean value theorem in invexity analysis

p r invex sets and functions abstract notions of invexity of a function and of a set are generalized the notion of an invex function with respect to can be further extended with the aid of p invex sets slight generalization of the notion of p invex sets with respect to leads to a new class of functions a family of real functions called in general p r pre invex functions with respect to without differentiability or p r invex functions with respect to in the differentiable case is introduced some geometric properties of these classes of functions are derived sufficient optimality conditions are obtained for a nonlinear programming problem involving p r invex functions with respect to

some advanced concepts in discrete aerodynamic sensitivity analysis abstract 1 0 introduction an efficient incremental iterative approach for dif ferentiating advanced flow codes is successfully demon strated on a 2d inviscid model problem the methodemploys the reverse mode capability of the automatic differentiation software tool adifor 3 0 and isproven to yield accurate first order aerodynamic sensi tivity derivatives a substantial reduction in cpu timeand computer memory is demonstrated in comparisonwith results from a straight forward black box t everse mode application of adifor 3 0 to the same flowcode an adifor assisted procedure for accurate sec ond order aerodynamic sensitivity derivatives is suc cessfidly verified on an inviscid transonic lifting airfoilexample problem the method requires that first orderderivatives are calculated first using both the fonvard direct and reverse adjoint procedures then a veryefficient non iterative calculation of all second orderderivatives can be accomplished accurate second de rivatives le the complete hessian matrices of lift wave drag and pitching moment coefficients are calcu lated with respect to geometric shape angle of attack and freestream mach numbercomputing sensitivity derivatives sds from high fidelity nonlinear cfd codes is an enabling technologyfor design of advanced concept vehicles in recent yearssignificant progress has been achieved in the efficientcalculation of accurate sds from these cfd codes the automatic differentiation ad software tooladifor automatic differentiation of fortran has been proven an effective tool for extracting aerody namlc

nonsmooth multiobjective optimization using limiting subdifferentials in this study using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem some weak pareto optimality necessary and sufficient conditions for nonsmooth multiobjective optimization problems are proved

adjoint a posteriori error measures for anisotropic mesh optimisation in this paper an adjoint or sensitivity based error measure is formulated which measures the error contribution of each solution variable to an overall goal the goal is typically embodied in an integral functional e g the solution in a small region of the domain of interest the resulting a posteriori error measures involve the solution of both primal and adjoint problems a comparison of a number of important a posteriori error measures is made in this work there is a focus on developing relatively simple methods that refer to information from the discretised equation sets often readily accessible in simulation codes and do not explicitly use equation residuals this method is subsequently used to guide anisotropic mesh adaptivity of tetrahedral finite elements mesh adaptivity is achieved here with a series of optimisation heuristics of the landscape defined by mesh quality mesh quality is gauged with respect to a riemann metric tensor embodying an a posteriori error measure such that an ideal element has sides of unit length when measured with respect to this metric tensor this results in meshes in which each finite element node has approximately equal subject to certain boundary conforming constraints and the performance of the mesh optimisation heuristics error contribution to the functional goal

on p r invexity type nonlinear programming problems abstract mathematical programming problems involving p r invex functions with respect to are considered we introduce new classes of nonlinear programming problems called kt p r invex wd p r invex and hc p r invex problems where p r are some real numbers it is shown that for these types of problems kuhn tucker conditions are both necessary and sufficient for optimality furthermore these p r invexity type problems with r 0 are not sufficient for wolfe weak duality in this way it was shown that the optimization problems possessing some kind of invexity need not be equivalent to the class of optimization problems for which kuhn tucker necessary conditions for optimality are also sufficient and wolfe weak duality holds

three dimensional aerodynamic shape optimization using discrete sensitivity analysis an aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three dimensional geometries the function of sensitivity analysis is to directly couple computational fluid dynamics cfd with numerical optimization techniques which facilitates the construction of efficient direct design methods the development of a practical three dimensional design procedures entails many challenges such as 1 the demand for significant efficiency improvements over current design methods 2 a general and flexible three dimensional surface representation and 3 the efficient solution of very large systems of linear algebraic equations it is demonstrated that each of these challenges is overcome by 1 employing fully implicit newton methods for the cfd analyses 2 adopting a bezier bernstein polynomial parameterization of two and three dimensional surfaces and 3 using preconditioned conjugate gradient like linear system solvers whereas each of these extensions independently yields an improvement in computational efficiency the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use the new aerodynamic shape optimization procedure is demonstrated in the design of both two and three dimensional inviscid aerodynamic problems including a two dimensional supersonic internal external nozzle two dimensional transonic airfoils resulting in supercritical shapes three dimensional transport wings and three dimensional supersonic delta wings each design application results in realistic and useful optimized shapes

characterization of nonsmooth quasiconvex and pseudoconvex functions this paper characterizes the nonsmooth quasiconvex and pseudoconvex functions using the properties of limiting subdifferentials

a mean value theorem in asplund spaces abstract in this paper a nonsmooth mean value theorem in asplund spaces under invexity is provided

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

p r invexity in multiobjective programming abstract in this paper a generalization of convexity namely p r invexity is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable the assumptions on pareto solutions are relaxed by means of p r invex functions also some duality results are obtained for such optimization problems

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

infinite semi infinite problems to characterize the optimality of nonlinear optimization problems considering a generic nonlinear programming problem nlpp this paper provides a family of linear infinite problems lips or linear semi infinite problems lsips and establishes the connection between optimality in the respective nlpp and that in the provided lips lsips

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

a sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms we present a sensitivity and adjoint calculus for the control of entropy solutions of scalar conservation laws with controlled initial data and source term the sensitivity analysis is based on shift variations which are the sum of a standard variation and suitable corrections by weighted indicator functions approximating the movement of the shock locations based on a first order approximation by shift variations in l1 we introduce the concept of shift differentiability which is applicable to operators having functions with moving discontinuities as images and implies differentiability for a large class of tracking type functionals in the main part of the paper we show that entropy solutions are generically shift differentiable at almost all times t 0 with respect to the control hereby we admit shift variations for the initial data which allows us to use the shift differentiability result repeatedly over time slabs this is useful for the design of optimization methods with time domain decomposition our analysis especially of the shock sensitivity combines structural results by using generalized characteristics and an adjoint argument our adjoint based shock sensitivity analysis does not require us to restrict the richness of the shock structure a priori and admits shock generation points the analysis is based on stability results for the adjoint transport equation with discontinuous coefficients satisfying a one sided lipschitz condition as a further main result we derive and justify an adjoint representation for the derivative of a large class of tracking type functionals

continuous time optimization problems involving invex functions in d h martin the essence of invexity j optim theory appl 47 1985 65 76 martin introduced the notions of kkt invexity and wd invexity for mathematical programming problems these notions are relaxations of invexity in this work we generalize these concepts for continuous time nonlinear optimization problems we prove that the notion of kkt invexity is a necessary and sufficient condition for global optimality of a karush kuhn tucker point and that the notion of wd invexity is a necessary and sufficient condition for weak duality

the gap function for optimization problems in banach spaces abstract in this paper some properties of the gap function for multiple objective optimization problems in banach spaces are established

numerical and theoretical considerations for sensitivity calculation of discontinuous flow abstract linearization of 1 d euler equations about a discontinuous solution is discussed from both the theoretical and numerical point of view estimates for the norm of the solution of the linearized system are shown to be valid for the case presented numerically the linearization is performed following the guidelines of tangent linear model and sensitivities with respect to a flow parameter are computed being in better agreement with the analytical value when compared with previously reported numerical results