We suggest a branch and bound algorithm for solving continuous optimization problems where a (generally nonconvex) objective function is to be minimized under nonconvex inequality constraints which satisfy some specific solvability assumptions. The assumptions hold for some special cases of nonconvex quadratic optimization problems. We show how the algorithm can be applied to the problem of min...

where x ∈ N is a vector of decision or choice variables, α ∈ A is a vector of parameters, f (·) is the twice continuously differentiable objective function, that is, f (·) ∈ C (2), and φ(·) is the indirect or maximized objective function. This is terminology you should be more or less familiar with from prior courses. Because we will deal repeatedly with vectors and matrices as well as the deri...

We define the distributed, continuous-time combinatorial optimization problem. We propose a general, semantically well-defined notion of solution stability in such systems, based on the cost of change from an already implemented solution to the new one. This approach allows maximum flexibility in specifying these costs through the use of stability constraints. We present the first mechanism for...

We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us to derive the no-regret properties of a large class of discretetime algorithms including as special cases the exponential weight algorithm, online mirror desc...

A Real-Time Optimization (RTO) strategy incorporating the fuzzy sets theory is developed, where the problem constraints obtained from process considerations are treated in fuzzy environment. Furthermore, the objective function is penalized by a fuzzified form of the key process constraints. To enable using conventional optimization techniques, the resulting fuzzy optimization problem is the...

Consolidation carriers transport shipments that are small relative to trailer capacity. To be cost-effective, the carrier must consolidate shipments, which requires coordinating their paths in both space and time, i.e., the carrier must solve a Service Network Design problem. Most service network design models rely on discretization of time, i.e., instead of determining the exact time at which ...

The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of co...

vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. this paper presents a bi-objective mathematical mod...