Derivative-free methods for mixed-integer nonsmooth constrained optimization

Computational Optimization and Applications - In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the...     

Hyperpigmentation induced by topical 5-aminolaevulinic acid plus visible light

Photodynamic therapy (PDT) with 5-aminolaevulinic acid (ALA) is an alternative tool for the treatment of superficial non-melanoma skin cancers. Recently ALA-PDT has been employed with encouraging results also for warts, condylomata and psoriasis. In this study the effects of topical ALA plus irradiation with visible light on intact human skin have been evaluated. Five skin areas (A, B, C, D, and E) on the inner upper part of the arms of five healthy volunteers (skin types III and IV) were treated with (A) ALA 20% in base cream without irradiation, (B) only the vehicle (base cream) without ALA, (C, D and E) ALA cream at the concentrations of 5, 10 and 20%, respectively; all treatments were applied with an occlusive dressing. Four hours after ALA or vehicle application areas B, C, D and E were irradiated with a fixed dose of 40 J/cm(2). ALA penetration through the intact skin was evaluated by in vivo fluorescence determination. The effects on healthy skin were evaluated by clinical and chromometric examinations, light microscopy, immunohistochemistry and electron microscopy. RESULTS: (1) in vivo fluorescence demonstrated that ALA is able to penetrate through the intact skin, when applied with occlusive dressing and induces a classical fluorescence peak due to Protoporphyrin IX (PpIX) formation, which is the active photosensitiser. (2) Skin areas receiving ALA plus irradiation showed erythema and swelling just after the irradiative session and hyperpigmentation 48-72 h later. (3) Colourimetric data confirmed significant skin colour changes: values a* (representing the erythematous changes) increased only on the skin areas where ALA+irradiation were applied and during the 48 h after irradiation, thereafter a* began to decrease; values L* (pigmentation) increased during the 2 weeks following treatment. (4) Histopathological, immunohistochemical (S100, HMB-45) and electron microscopic findings showed an absolute increment of the number of melanocytes, which appeared clearly activated. In conclusion the application of ALA cream followed by irradiation is able to induce a pigmentation response in healthy human skin, at least in skin types III and IV. This melanocytic activation could have a potential for the treatment of skin disorders characterised by hypopigmentation.     

A truncated Newton method in an augmented Lagrangian framework for nonlinear programming

In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate.     

A magnetic resonance device designed via global optimization techniques

In this paper we are concerned with the design of a small low-cost, low-field multipolar magnet for Magnetic Resonance Imaging with a high field uniformity. By introducing appropriate variables, the considered design problem is converted into a global optimization one. This latter problem is solved by means of a new derivative free global optimization method which is a distributed multi-start type algorithm controlled by means of a simulated annealing criterion. In particular, the proposed method employs, as local search engine, a derivative free procedure. Under reasonable assumptions, we prove that this local algorithm is attracted by global minimum points. Additionally, we show that the simulated annealing strategy is able to produce a suitable starting point in a finite number of steps with probability one.This work was supported by CNR/MIUR Research Program Metodi e sistemi di supporto alle decisioni, Rome, Italy.Mathematics Subject Classification (1991):65K05, 62K05, 90C56     

A partition-based global optimization algorithm

This paper is devoted to the study of partition-based deterministic algorithms for global optimization of Lipschitz-continuous functions without requiring knowledge of the Lipschitz constant. First we introduce a general scheme of a partition-based algorithm. Then, we focus on the selection strategy in such a way to exploit the information on the objective function. We propose two strategies. The first one is based on the knowledge of the global optimum value of the objective function. In this case the selection strategy is able to guarantee convergence of every infinite sequence of trial points to global minimum points. The second one does not require any a priori knowledge on the objective function and tries to exploit information on the objective function gathered during progress of the algorithm. In this case, from a theoretical point of view, we can guarantee the so-called every-where dense convergence of the algorithm.     

A Truncated Newton Method for the Solution of Large-Scale Inequality Constrained Minimization Problems

A new active set Newton-type algorithm for the solution of inequality constrained minimization problems is proposed. The algorithm possesses the following favorable characteristics: (i) global convergence under mild assumptions; (ii) superlinear convergence of primal variables without strict complementarity; (iii) a Newton-type direction computed by means of a truncated conjugate gradient method. Preliminary computational results are reported to show viability of the approach in large scale problems having only a limited number of constraints.     

Hypericin photosensitization of tumor and metastatic cell lines of human prostate

We have investigated the photoactivating effect of hypericin on two cancer cell lines: PC-3, a prostatic adenocarcinoma non-responsive to androgen therapy and LNCaP, a lymphonodal metastasis of prostate carcinoma responsive to androgen therapy. The two cell lines are incubated for 24 h with hypericin at concentrations ranging from 0.001 to 0.3 microg/ml in cell culture medium. The cells are irradiated at 599 nm (fluence = 11 J/cm2) using a dye laser pumped by an argon laser. Hypericin exerts phototoxic effects on both cell lines, while it does not produce toxic effects in the absence of irradiation. These results suggest that photodynamic therapy (PDT) with hypericin could be an alternative approach to the treatment of prostatic tumors, and could be beneficial in tumors that are non-responsive to androgen therapy.