Approximation of the Quadratic Knapsack Problem

We study the approximability of the classical quadratic knapsack problem (QKP) on special graph classes. In this case the quadratic terms of the objective function are not given for each pair of knapsack items. Instead an edge weighted graph G = (V,E) whose vertices represent the knapsack items induces a quadratic profit p_ij for the … Read more

Reactive Power Management using Firefly and Spiral Optimization under Static and Dynamic Loading Conditions

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

A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil

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

Polynomial time algorithms for the Minimax Regret Uncapacitated Lot Sizing Model

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

Trust Region Subproblem with a Fixed Number of Additional Linear Inequality Constraints has Polynomial Complexity

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

Turnpike theorems for convex problems with undiscounted integral functionals

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

Optimal control modeling of cell division

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