On calmness of a class of multifunctions

The paper deals with calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various calmness criteria which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmoooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there

Variational Analysis of Marginal Functions with Applications to Bilevel Programming

This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces

On Hölder calmness of minimizing sets

We present conditions for Hölder calmness and upper Hölder continuity of optimal solution sets to perturbed optimization problems in finite dimensions. Studies on Hölder type stability were a popular subject in variational analysis already in the 1980s and 1990s, and have become a revived interest in the last decade. In this paper, we focus on conditions for Hölder calmness of the argmin mapping in the case of non-isolated minima. We recall known ideas and results in this context for general as well as special parametric programs, refine them and discuss particular settings, including nonlinear programs and convex semi-infinite optimization problems

Resolution enhancement of multichannel microwave imagery from the Nimbus-7 SMMR for maritime rainfall analysis

A restoration of the 37, 21, 18, 10.7, and 6.6 GHz satellite imagery from the scanning multichannel microwave radiometer (SMMR) aboard Nimbus-7 to 22.2 km resolution is attempted using a deconvolution method based upon nonlinear programming. The images are deconvolved with and without the aid of prescribed constraints, which force the processed image to abide by partial a priori knowledge of the high-resolution result. The restored microwave imagery may be utilized to examined the distribution of precipitating liquid water in marine rain systems

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called \$M\$-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify \$M\$-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify M-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration

Development and Application of a Potential Flow Computer Program: Determining First and Second Order Wave Forces at Zero and Forward Speed in Deep and Intermediate Water Depth

A ship traveling in irregular sea with a steady forward speed is a classical hydrodynamics problem which still presents many challenges. An in-house computational code MDLHydroD based on potential theory has been developed to address this problem. A Green function based approach is followed in frequency domain to obtain the linear forces and motion of the vessel. A perturbation approach is then applied to extract the second order forces, and the added resistance on the ship is thus obtained. The numerical method is then extended to consider finite water depth effects. A new finite depth Green function is developed and implemented in the 3D potential code. This allowed analysis of ship motion with forward speed in intermediate water depths. An optimization framework is then developed to solve the inverse problem of ship hull optimization which is classified as a multi variable multi objective problem with nonlinear constraints. The three main problems encountered in the inverse design of ship hull are: automated geometry creation, prediction of forces due to fluid structure interaction and modifying the hull towards a better performing hull form. For this study, a parametric hull form based on typical ship parameters is developed which can be altered to obtain different ship hulls that can be analyzed using the developed hydrodynamic code MDLHydroD. A number of different optimization solvers are studied to understand and select appropriate solver for ship hull optimization. Solvers based on evolutionary algorithms were found to be adequate and used to demonstrate the capabilities of the hull optimization framework. Both single and multi-objective optimization algorithms are implemented. A selected optimized design from the Pareto front is then compared with initial design to show the effectiveness of the optimization method. This study will provide a thorough analysis of hydrodynamic load prediction methodologies and its application in obtaining safer, fuel efficient and more stable hull forms