Free material optimization.
Fritz John's type conditions and associated duality forms in convex non differentiable vector-optimization
Frobenius numbers by lattice point enumeration.
From Eckart and Young approximation to Moreau envelopes and vice versa
In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.
From scalar to vector optimization
Initially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem , , are given. These conditions work with arbitrary functions , but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It...
Full approximability of a class of problems over power sets.
In this paper results concerning structural and approximability properties of the subclass of NP-Complete Optimization Problems, defined over a lattice are considered. First, various approaches to the concept of Fully Polynomial Approximation Scheme are presented with application to several known problems in the class of NP-Complete Optimization Problems.Secondly, a characterization of full Approximability for the class of Max Subset Problems is introduced.
Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds
In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...
Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds
In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...
Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds
In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from Euclidean spaces to Hadamard manifolds and prove that, in the convex case, these concepts coincide with the classical one. For the minimization problem, assuming that the function is bounded from below, in the quasiconvex and lower semicontinuous...
Full-Newton step infeasible interior-point algorithm for SDO problems
In this paper we propose a primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main step of the algorithm consists of a feasibility step and several centering steps. At each iteration, we use only full-Newton step. Moreover, we use a more natural feasibility step, which targets at the -center. The iteration bound of the algorithm coincides...
Funciones penalidad y lagrangianos aumentados.
Por medio de un conjunto de propiedades se caracteriza una amplia familia de funciones que pueden emplearse como penalidad para la resolución numérica de un problema de programación matemática. A partir de ellas se construye un algoritmo de penalizaciones demostrando su convergencia a un punto factible óptimo. Se estudia la situación de los mínimos sin restricciones respecto de la región factible, la monotonía de la sucesión de valores de la función auxiliar y se dan varias cotas de convergencia....
Functional equations in dynamic programming.
Funzioni semiconcave, singolarità e pile di sabbia
La semiconcavità è una nozione che generalizza quella di concavità conservandone la maggior parte delle proprietà ma permettendo di ampliarne le applicazioni. Questa è una rassegna dei punti più salienti della teoria delle funzioni semiconcave, con particolare riguardo allo studio dei loro insiemi singolari. Come applicazione, si discuterà una formula di rappresentazione per la soluzione di un modello dinamico per la materia granulare.
Further study on strong Lagrangian duality property for invex programs via penalty functions.
Fuzzy Evaluation Method Using Fuzzy Rule Approach in Multicriteria Analysis
Fuzzy Goal Programming for Agricultural Land Allocation Problems
Fuzzy Linear Fractional Set Covering Problem with Imprecise Costs
Set covering problems are in great use these days, these problems are applied in many disciplines such as crew scheduling problems, location problems, testing of VLSI circuits, artificial intelligence etc. In this paper α-acceptable optimal solution is given for the fuzzy linear fractional set covering problem where fuzziness involved in the objective function. At first the fuzzy linear fractional problem is being converted in to crisp parametric linear fractional set covering problem then a linearization...
Fuzzy linear programming via simulated annealing
This paper shows how the simulated annealing (SA) algorithm provides a simple tool for solving fuzzy optimization problems. Often, the issue is not so much how to fuzzify or remove the conceptual imprecision, but which tools enable simple solutions for these intrinsically uncertain problems. A well-known linear programming example is used to discuss the suitability of the SA algorithm for solving fuzzy optimization problems.
Fuzzy linguistic optimization on surface roughness for CNC turning.
Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem
In this paper, a solution procedure is proposed to solve fuzzy linear fractional programming (FLFP) problem where cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. Here, the FLFP problem is transformed into an equivalent deterministic multi-objective linear fractional programming (MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective linear programming (LP) problem. The proposed...