Nesterov and Todd discuss several path-following and potential-reduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how to take Mehrotra predictor-corrector steps in this framework. We also provide some computational results suggesting that our algorithm is more robust than alternative methods.

We discuss several di#erent search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, HelmbergRendl -Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also. Key words: semidefinite programming, search direction, invariance properties. AMS Subject classification: 90C05. Abbreviated title: Search directions in SDP 1 Introduction This paper is concerned with interior-point methods for semidefinite programming (SDP) problems and in particular the various search directions they use and ...

propose to use an extended Gaussian imap,e (EGI) for interpreting 2-1/2-D representations for recognition of 3-D objects. The EGI is constructed by mapping each surface normals of an object to the Gaussian sphere. The freedom in viewer directions caused by incomplete observation Is greatly reduced by applying constraints derived from a global distribution of surface normals on the EGI. One constraint on the viewer direction is derived from the ratio of the projected area to the original surface area. The other constraint comes from the direction of the principal axis. After reducing the possible viewing directions with these constraints, we will apply a matching function to ESls of a candidate set for a final decision. We also propose an algorithm for reconstruction of the original shape of a convex polyhedron from its EGI. This algorithm is based on the analysis-by-synthesis method. 1 WHAT IS THE EXTENDED GAUSSIAN IMAGE A collection of local surface normals [1,2,3,4,5], sometimes referred to as a 2-1/2-D representation of an object [6], is often provided by machine vision at the low level. For example, an algorithm based on the propagation-of-constraints technique [2] provides local surface orientation from shading and occluding information. The same algorithm can also produce surface orientation from apparent distortion of known patterns based on a regular-pattern gradient map [A], The distortion of these small circles on the golf ball in Fig. 1 can be used to recover local surface orientation.

Adding a sharing method to a genetic algorithm promotes the formation and maintenance of stable subpopulations. This paper explores the limits of sharing by deriving closed-form expressions for the expected time to disappearance of a subpopulation. The time to disappearance is shown to be an exponential function of population size, with relative subpopulation fitnesses determining the base of the exponential. However, disappearance time decreases rapidly as the number of subpopulations increases. Both theoretical and experimental illustrations are given of genetic drift in sharing. I. Introduction Given a problem with multiple solutions, the traditional genetic algorithm (GA) will at best, ultimately converge to a population containing only one of those solutions [1]. The culprit, known as genetic drift, can be defined as the convergence of a finite population in the absence of selection pressure, due to variance in the selection process. To combat genetic drift, GAs were developed t...

Abstract. We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability distribution depending on the previous state and on the pair of actions chosen by the players. Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs. Therefore, if two partial plays are indistinguishable by some player, he should behave the same in both of them. We consider reachability (does the play eventually visit a final state?) and Büchi objective (does the play visit infinitely often a final state?). Our main contribution is to prove that the following problem is complete for 2-ExpTime: decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her oponent. We also characterise those strategies needed by the first player to almost-surely win. 1