Employing different loss functions for the classification of images via supervised learning

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.     

Duality for location problems with unbounded unit balls

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the “distances” are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

Proximal-gradient algorithms for fractional programming

In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-?ojasiewicz property.     

Vectorial penalization for generalized functional constrained problems

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.     

On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization

The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new.     

A fluorescence anisotropy method for measuring protein concentration in complex cell culture media

The rapid, quantitative analysis of the complex cell culture media used in biopharmaceutical manufacturing is of critical importance. Requirements for cell culture media composition profiling, or changes in specific analyte concentrations (e.g. amino acids in the media or product protein in the bioprocess broth) often necessitate the use of complicated analytical methods and extensive sample handling. Rapid spectroscopic methods like multi-dimensional fluorescence (MDF) spectroscopy have been successfully applied for the routine determination of compositional changes in cell culture media and bioprocess broths. Quantifying macromolecules in cell culture media is a specific challenge as there is a need to implement measurements rapidly on the prepared media. However, the use of standard fluorescence spectroscopy is complicated by the emission overlap from many media components. Here, we demonstrate how combining anisotropy measurements with standard total synchronous fluorescence spectroscopy (TSFS) provides a rapid, accurate quantitation method for cell culture media. Anisotropy provides emission resolution between large and small fluorophores while TSFS provides a robust measurement space. Model cell culture media was prepared using yeastolate (2.5 mg mL^–1) spiked with bovine serum albumin (0 to 5 mg mL^–1). Using this method, protein emission is clearly discriminated from background yeastolate emission, allowing for accurate bovine serum albumin (BSA) quantification over a 0.1 to 4.0 mg mL^–1range with a limit of detection (LOD) of 13.8 μg mL^–1.