In this paper some concepts and techniques of Mathematical Programming are extended in an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex functions, variational problem and monotone vector fields are extended to the sphere and several characterizations of these notions are shown. As an application of the convexity concept, necessary and sufficient optim...

If one wants to minimize a nonlinear functional it is often fruitful to consider the relationships which must hold at a minimum If the functional is di erentiable and the permitted variations at the minimum constitute a linear space this process gives equations that the minimum must satisfy and if the functional is quadratic these equations are linear However if the set of permitted variations ...

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of ...

In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such are useful in various physical and geometric applications. Our formulas compute the difference indices two Hessians related to different graphs or sets boundary conditions. Several applications such as iteration lower bounds proved.

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

Using the technique of variational analysis and in terms of normal cones, we establish unified separation results for finitely many closed (not necessarily convex) sets in Banach spaces, which not only cover the existing nonconvex separation results and a classical convex separation theorem but also recapture the approximate projection theorem. With help of the separation result for closed sets...

The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems in finite-dimensional and infinite-dimensional spaces. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization. Based on second-order generalized diff...

We develop a general variational framework for the finite element solution of the pure Neumann problem. Our starting point is the equivalence between the weak Neumann equation and a minimization problem on the factor space H1(Ω)/RI . This problem gives rise to a family of minimization problems posed on conventional Sobolev spaces but constrained by a generalized zero-mean condition. We show tha...

In this paper we consider optimal sampled-data control problems on time scales with inequality state constraints. A Pontryagin maximum principle is established, extending to the constrained case existing results in scale literature. The proof based Ekeland variational and concept of implicit spike variations adapted setting. main result then applied continuous-time min-max problems, a maximal v...