In this paper, we propose new linesearch-based methods for nonsmooth constrained optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequal...

Caching, symmetries, and search with decomposition are powerful techniques for pruning the search space of constraint problems. In this paper we present an innovative way of efficiently combining these techniques with branch and bound for solving certain types of constraint optimization problems (COPs). Our new method significantly reduces the overhead of performing decomposition during search ...

Constraint optimization underlies many problems in AI. We present a novel algorithm for finite domain constraint optimization that generalizes branch-and-bound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can be represented implicitly and compactly using symbolic techniques such as decision diagrams, the s...

Branch and bound is an effective technique for solving constraint optimization problems (COP’s). However, its search space expands very rapidly as the domain sizes of the problem variables grow. In this paper, we present an algorithm that clusters the values of a variable’s domain into sets. Branch and bound can then branch on these sets of values rather than on individual values, thereby reduc...

In validated branch and bound algorithms for global optimization, upper bounds on the global optimum are obtained by evaluating the objective at an approximate optimizer; the upper bounds are then used to eliminate subregions of the search space. For constrained optimization, in general, a small region must be constructed within which existence of a feasible point can be proven, and an upper bo...

An overview of interval arithmetical tools and basic techniques is presented that can be used to construct deterministic global optimization algorithms. These tools are applicable to unconstrained and constrained optimization as well as to nonsmooth optimization and to problems over unbounded domains. Since almost all interval based global optimization algorithms use branch-and-bound methods wi...