Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εk-global minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an ε-global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.

Abstract. Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. At the core of many of these applications is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal feasible solution. In the arena of model-based autonomy, deep space probes have given way to more agile vehicles, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, carried from the conflict-directed search algorithm in model-based reasoning. We introduce a novel algorithm called Generalized Conflict-Directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or suboptimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. Evaluated empirically on a range of test problems of coordinated air vehicle control, GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm applied to either disjunctive linear programs or an equivalent binary integer programming encoding. 1

Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies, and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints. Then, it introduces a generalization of Quad to polynomial constraint systems. It also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system. Different linearization techniques are investigated to limit the number of generated constraints. QuadSolver, a new branch and prune algorithm that combines Quad, local consistencies, and interval methods, is introduced. QuadSolver has been evaluated on a variety of benchmarks from kinematics, mechanics, and robotics. On these benchmarks, it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with state-of-the-art optimization solvers.

Abstract. In this article we describe EANT2, Evolutionary

Abstract We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital requirement for a portfolio of operational risk losses. Key words risk aggregation – dependency bounds – operational risk – mass transportation duality theorem – global optimization

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This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is taken to ensure that all methods correctly account for rounding errors in the computations.

symmetrydetection andexploitation

In this paper, we develop a convexification tool that enables the construction of convex hulls for orthogonal disjunctive sets using convex extensions and disjunctive programming techniques. A distinguishing feature of our technique is that, unlike most applications of disjunctive programming, it does not require the introduction of new variables in the relaxation. We develop and apply a toolbox of results that help in checking the technical assumptions under which the convexification tool can be employed. We demonstrate its applicability in integer programming by deriving the intersection cut for mixed-integer polyhedral sets and the convex hull of certain mixed/pure-integer bilinear sets. We then develop a key result that extends the applicability of the convexification tool to relaxing nonconvex inequalities, which are not naturally disjunctive, by providing sufficient conditions for establishing the convex extension property over the non-negative orthant. We illustrate the utility of this result by deriving the convex hull of a continuous bilinear covering set over the non-negative orthant. 1