Conventional ways of using local search are diicult to generalize. Increased eeciency is the only goal, generality often being disregarded. This is manifested in the highly monolithic encodings of complex problems and the application of highly speciic satisfaction methods. Other approaches take the general constraint programming framework as a starting point and try to introduce local search me...

To everyone who loves mathematics, everywhere. i Acknowledgements I cannot stress enough how wonderful it is to study mathematics at Berkeley. I had the great privilege to share ideas there with many fantastic mathematicians. My advisor, Ken Ribet, granted me the freedom to pursue this project while masterfully answering the lion's share of my questions. The ideas for the final chapter grew out...

A new hypergraph coloring problem is introduced by de ning N(H; e) as the maximal number of colors in a vertex coloring of a hypergraph H = (V; E) , which has not more than e di erent colors in every edge. Our main results concern the asymptotic behaviour of this quantity for the uniform hypergraph H(n; `; k) = (V(n; `); E(n; `; k)) with vertex set V(n; `) = ǹ for n = f1; 2; : : : ; ng and edge...

Local Constraints in Combinatorial Optimization

We show how to compute lower bounds for the maximum possible Bayes error if the class-conditional distributions must satisfy moment constraints. Our approach makes use of Curto and Fialkow’s solutions for the truncated moment problem. We also give an upper bound that follows from related work by Lanckreit et al., Bertsimas and Popescu, and Marshall and Olkin. Index Terms Bayes error, maximum en...

Effect of level statistics on local electronic states and local magnetism in nanoscale metallic grains with transition-metal impurity in the ballistic regime is studied. It is shown that the mean occupation of local electron and the local magnetic moment in nanoscale metallic grains with odd conduction-electrons are larger than those with even conduction-electrons. The effect of even-odd parity...

In models defined by unconditional moment restrictions, specification tests are possible and estimators can be ranked in terms of efficiency whenever the number of moment restrictions exceeds the number of parameters. We show that a similar relationship between potential refutability of a model and semiparametric efficiency is present in a much broader class of settings. Formally, we show a con...

This paper is concerned with some feasibility issues in mathematical programs with equilibrium constraints (MPECs) where additional joint constraints are present that must be satis ed by the state and design variables of the problems. We introduce su cient conditions that guarantee the feasibility of these MPECs. It turns out that these conditions also guarantee the feasibility of the quadratic...