Many difficult computational problems involve the simultaneous satisfaction
of multiple constraints which are individually easy to satisfy. Such problems
occur in diffractive imaging, protein folding, constrained optimization (e.g.,
spin glasses), and satisfiability testing. We present a simple geometric
framework to express and solve such problems and apply it to two benchmarks. In
the first application (3SAT, a boolean satisfaction problem), the resulting
method exhibits similar performance scaling as a leading context-specific
algorithm (walksat). In the second application (sphere packing), the method
allowed us to find improved solutions to some old and well-studied optimization
problems. Based upon its simplicity and observed efficiency, we argue that this
framework provides a competitive alternative to stochastic methods such as
simulated annealing.Comment: 4 pages, 2 figure