Results 1  10
of
12
A feasible BFGS interior point algorithm for solving strongly convex minimization problems
 SIAM J. OPTIM
, 2000
"... We propose a BFGS primaldual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of posit ..."
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Cited by 13 (1 self)
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We propose a BFGS primaldual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters µ converging to zero. We prove that it converges qsuperlinearly for each fixed µ. We also show that it is globally convergent to the analytic center of the primaldual optimalset when µ tends to 0 and strict complementarity holds.
Automatic Differentiation applied to a Nonsmooth Optimization Problem
 In Numerical Methods in Engineering ’96
, 1996
"... . There are many situations where one has to minimize a nonlinear cost function f that is differentiable or at least admits gradients almost everywhere. In this paper, we outline optimization algorithms that rely on explicit computations of gradients or limits of gradients, using specific automatic ..."
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Cited by 4 (0 self)
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. There are many situations where one has to minimize a nonlinear cost function f that is differentiable or at least admits gradients almost everywhere. In this paper, we outline optimization algorithms that rely on explicit computations of gradients or limits of gradients, using specific automatic differentiation techniques. We consider functions represented by Fortran programs. We suppose that singularities are consequences either of "branching" operations (absolute value, max, conditional structures with simple tests) or of classical elementary functions (square root when computing an Euclidean norm), which generate kinks where f admits a directional derivative in any direction. We present algorithms and implementations on top of the automatic differentiation system Odyss'ee to compute directional derivatives and limits of gradients that allow descriptions of normal cones. Together with the input Fortran code, this is used by our optimization library Odymin to minimize f . We presen...
Computation of High Order Derivatives in Optimal Shape Design
, 1994
"... this paper we study higher order derivatives. But one can ask the following questions:  are they expensive to calculate?  are they complicated to use?  are they imprecise?  are they useless? At first sight, the answer seems to be positive, but classical results of V. Strassen [20] and J. Mor ..."
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Cited by 2 (1 self)
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this paper we study higher order derivatives. But one can ask the following questions:  are they expensive to calculate?  are they complicated to use?  are they imprecise?  are they useless? At first sight, the answer seems to be positive, but classical results of V. Strassen [20] and J. Morgenstern [13] tell us that the higher order derivatives are not expensive to calculate, and can be computed automatically. The purpose of this paper is to give an answer to the third question by proving that the higher order derivatives of a function can be computed with the same precision as the function itself. We prove also that the derivatives so computed are equal to the derivatives of the discrete problem (see Diagram 1). We call the discrete problem the finite dimensional problem processed by the computer. This result allows the use of automatic differentiation ([5], [6]), which works only on discrete problems. Furthermore, the computations of Taylor's expansions which are proposed at the end of this paper, could be a partial answer to the last question.
Kaltofen’s divisionfree determinant algorithm differentiated
"... for matrix adjoint computation ..."
Reducing sensitivity analysis timecost of compound model
 IEEE Trans. Magn
, 2004
"... Abstract—This paper deals with the sensitivity analysis of compound models in the case of gradient based optimization. Multidisciplinary optimization (MDO) may use timeconsuming analysis such as the finiteelement method (FEM) resolution, their sensitivity analysis must then be managed efficiently ..."
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Cited by 1 (1 self)
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Abstract—This paper deals with the sensitivity analysis of compound models in the case of gradient based optimization. Multidisciplinary optimization (MDO) may use timeconsuming analysis such as the finiteelement method (FEM) resolution, their sensitivity analysis must then be managed efficiently in order to limit their evaluations. A composition model implementation based on differential propagation mechanism has been used. Different solutions of sensitivity analysis based on forward finite difference are proposed at the level of each inner model. These solutions have been implemented for the design of a transformer, using mixed modeling (FEM + analytic). It has led to a reduction by a factor of two then three of an optimization iteration time cost. Index Terms—Finite difference, mixed model, optimization, sensitivity computation, transformer design. I.
A New Global Optimization Algorithm
, 1996
"... . We present a new global optimization method and one of its applications to an eigenvalue problem. We will prove the convergence of this algorithm. This algorithm is based on automatic differentiation and the higher order derivative method. It consists in approaching the cost function by a Taylor' ..."
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. We present a new global optimization method and one of its applications to an eigenvalue problem. We will prove the convergence of this algorithm. This algorithm is based on automatic differentiation and the higher order derivative method. It consists in approaching the cost function by a Taylor's expansion and in calculating the zeros of the derivatives. Using the Rellich theorem and solving several factorized linear systems, we calculate the eigenvalue/eigenvector derivatives. By this approach, we can apply this algorithm to an eigenvalue problem, here in quantum chemistry. AMS subject classification: 73K40, 65D25, 65F15, 65D15. Key words: Global optimization, Automatic differentiation, Higher order derivative method, Eigenvalue derivatives, Linear system. 1 Introduction. We introduce a new global optimization method whose idea is as follow : Using automatic differentiation and the higher order derivative method, we obtain an explicit solution of the cost function by a Taylor's...
Application of the automatic differentiation tool  Odyssee to a system of thermohydraulic equations
"... The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the ..."
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The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the automatic differentiator Odyssee with as few manual interventions as possible. The program to differentiate contains 23 subroutines, including linear solvers and blackbox functions, whose code is not available. 1
unknown title
"... Application of the automatic differentiation tool Odyssée to a system of thermohydraulic equations1 C. Duval2and P. Erhard2and Ch. Faure3and J.Ch. Gilbert4 Abstract. The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat ..."
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Application of the automatic differentiation tool Odyssée to a system of thermohydraulic equations1 C. Duval2and P. Erhard2and Ch. Faure3and J.Ch. Gilbert4 Abstract. The applicability of automatic differentiation on a set of partial differential equations governing thermohydraulic phenomena in heat exchangers is examined. More specifically, the challenge is to differentiate Thyc1D, a 1D mockup of the 3D code Thyc implementing these equations, by means of the automatic differentiator Odyssée with as few manual interventions as possible. The program to differentiate contains23subroutines, including linear solvers and blackbox functions, whose code is not available. 1
Languages, Algorithms
"... We present here transalpyne, a scripting language, to be executed on top of a computer algebra system, that is specifically conceived for automatic transposition of linear functions. Its type system is able to automatically infer all the possible linear functions realized by a computer program. The ..."
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We present here transalpyne, a scripting language, to be executed on top of a computer algebra system, that is specifically conceived for automatic transposition of linear functions. Its type system is able to automatically infer all the possible linear functions realized by a computer program. The key feature of transalpyne is its ability to transform a computer program computing a linear function in another computer program computing the transposed linear function. The time and space complexity of the resulting program are similar to the original ones.