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41.
42.
Q.J. Zhu 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1719-1736
Using the language of convex analysis, we describe key results in several important areas of finance: portfolio theory, financial derivative trading and pricing and consumption based asset pricing theory. We hope to emphasize the importance of convex analysis in financial mathematics and also draw the attention of researchers in convex analysis to interesting issues in financial applications. 相似文献
43.
Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this
class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied
by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained
by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or
equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty.
Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.
This research was supported by the Air Force Office of Scientific Research Grant AFOSR-83-0234 相似文献
44.
Donal O'Regan 《Journal of Mathematical Analysis and Applications》2005,309(2):383-391
In this paper we present a two-norms version of Krasnoselskii's fixed point theorem in cones. The abstract result is then applied to prove the existence of positive Lp solutions of Hammerstein integral equations with better integrability properties on the kernels. 相似文献
45.
We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards
feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and
subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which
constraints are positively homogeneous—so that zero is a natural Slater point—and an exact oracle may be time consuming. Finally,
our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated
on a number of cutting-stock problems.
Research supported by INRIA New Investigation Grant “Convex Optimization and Dantzig–Wolfe Decomposition”. 相似文献
46.
47.
We consider the method for constrained convex optimization in a Hilbert space, consisting of a step in the direction opposite to an
k
-subgradient of the objective at a current iterate, followed by an orthogonal projection onto the feasible set. The normalized stepsizes
k
are exogenously given, satisfying
k=0
k = ,
k=0
k
2
< , and
k is chosen so that
k k for some > 0. We prove that the sequence generated in this way is weakly convergent to a minimizer if the problem has solutions, and is unbounded otherwise. Among the features of our convergence analysis, we mention that it covers the nonsmooth case, in the sense that we make no assumption of differentiability off, and much less of Lipschitz continuity of its gradient. Also, we prove weak convergence of the whole sequence, rather than just boundedness of the sequence and optimality of its weak accumulation points, thus improving over all previously known convergence results. We present also convergence rate results. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research of this author was partially supported by CNPq grant nos. 301280/86 and 300734/95-6. 相似文献
48.
49.
We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ?2-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the l2 algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials. 相似文献
50.
Oscar Hernan Madrid-Padilla James Scott 《Journal of computational and graphical statistics》2017,26(3):537-546
We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features. 相似文献