We study the Minimax Regret Uncapacitated Lot Sizing (MRULS) model, where the production cost function and the demand are subject to uncertainty. We propose a polynomial time algorithm which solves the MRULS model in O(n^6) time. We improve this running time to O(n^5) when only the demand is uncertain, and to O(n^4) when only the … Read more
The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990’s. It is now understood that, under the primal Slater condition, (QP1QC) has a tight SDP relaxation (PSDP). The optimal solution to (QP1QC), if exists, can be obtained by … Read more
Power System planning encompasses the concept of minimization of transmission losses keeping in mind the voltage stability and system reliability. Voltage profile decides the state of a system and its control is dependent on Generator source voltage, shunt/series injection, transformer taps etc. Optimal parameter setting in system level is needed for managing the available resources … Read more
This paper investigates the population dynamics of a system of identically prepared B cells whose proliferation trajectories have been individually tracked using live-cell imaging techniques. The main goal is to investigate whether the system behavior can be determined using an optimality criterion. In order to achieve this goal we assume the existence of an intracellular … Read more
In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having convex graph. Utility function is concave but not necessarily strictly concave. The turnpike theorem is proved under the main assumption that over any given line segment, either multi-valued mapping is … Read more
The trust region subproblem with a fixed number m additional linear inequality constraints, denoted by (T_m), have drawn much attention recently. The question as to whether Problem ( T_m) is in Class P or Class NP remains open. So far, the only affirmative general result is that (T_1) has an exact SOCP/SDP reformulation and thus … Read more
We present a coarse-grain (outer-loop) parallel implementation of RLT1/2/3 (Level 1, 2, and 3 Reformulation and Linearization Technique—in that order) bound calculations for the QAP within a branch-and-bound procedure. For a search tree node of size S, each RLT3 and RLT2 bound calculation iteration is parallelized S ways, with each of S processors performing O(S5) … Read more
This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective … Read more
The augmented Lagrangian method (ALM) is a benchmark for solving convex minimization problems with linear constraints. When the objective function of the model under consideration is representable as the sum of some functions without coupled variables, a Jacobian or Gauss-Seidel decomposition is often implemented to decompose the ALM subproblems so that the functions’ properties could … Read more
Utilizing dual descriptions of the normal cone of convex optimization problems in conic form, we characterize the vertices of semidefinite representations arising from Lovász theta body, generalizations of the elliptope, and related convex sets. Our results generalize vertex characterizations due to Laurent and Poljak from the 1990’s. Our approach also leads us to nice characterizations … Read more