Stochastic Sequencing of Surgeries for a Single Surgeon Operating in Parallel Operating Rooms

We develop algorithms for a stochastic two-machine single-server sequencing problem with waiting time, idle time and overtime costs. Scheduling surgeries for a single surgeon operating in two parallel operating rooms (ORs) motivates the work. The basic idea is that staff perform cleanup and setup in one OR while the surgeon is operating in the other. … Read more

A probabilistic analysis of the strength of the split and triangle closures

In this paper we consider a relaxation of the corner polyhedron introduced by Andersen et al., which we denote by RCP. We study the relative strength of the split and triangle cuts of RCP’s. Basu et al. showed examples where the split closure can be arbitrarily worse than the triangle closure under a `worst-cost’ type … Read more

Two-Stage Robust Power Grid Optimization Problem

Under the deregulated energy market environment, plus the integration of renewable energy generation, both the supply and demand of a power grid system are volatile and under uncertainty. Accordingly, a large amount of spinning reserve is required at each bus to maintain the reliability of the power grid system in the traditional approach. In this … Read more

On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization

The (optimal) function/gradient evaluations worst-case complexity analysis available for the Adaptive Regularizations algorithms with Cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order and derivative free methods applied on the same problem class. A comparison with the results obtained for derivative-free methods by Vicente … Read more

SpeeDP: A new algorithm to compute the SDP relaxations of Max-Cut for very large graphs

We consider low-rank semidefinite programming (LRSDP) relaxations of unconstrained {-1,1} quadratic problems (or, equivalently, of Max-Cut problems) that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a new merit function … Read more

Fairer Benchmarking of Optimization Algorithms via Derivative Free Optimization

Research in optimization algorithm design is often accompanied by benchmarking a new al- gorithm. Some benchmarking is done as a proof-of-concept, by demonstrating the new algorithm works on a small number of dicult test problems. Alternately, some benchmarking is done in order to demonstrate that the new algorithm in someway out-performs previous methods. In this … Read more

A quasi-Newton strategy for the sSQP method for variational inequality and optimization problems

The quasi-Newton strategy presented in this paper preserves one of the most important features of the stabilized Sequential Quadratic Programming method, the local convergence without constraint qualifications assumptions. It is known that the primal-dual sequence converges quadratically assuming only the second-order sufficient condition. In this work, we show that if the matrices are updated by … Read more

Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures

We define a risk averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk averse formulation of the problem. This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of … Read more

Portfolio Selection under Model Uncertainty: A Penalized Moment-Based Optimization Approach

We present a new approach for portfolio selection when the underlying distribution of asset returns is uncertain or ambiguous to investors. In particular, we consider the case that an investor can formulate some reference financial models based on his/her prior beliefs or information, but is concerned about misspecification of the reference models and the associated … Read more

On the acceleration of augmented Lagrangian method for linearly constrained optimization

The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic development of constrained optimization. In this paper, we mainly show that Nesterov’s influential acceleration techniques can be applied to accelerate ALM, thus yielding an accelerated ALM whose iteration-complexity is O(1/k^2) for linearly constrained convex programming. As a by-product, we also show easily that … Read more