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

Categories Applications - Science and Engineering, Global Optimization Applications, Stochastic Programming Tags , , , ,

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

Optimal control modeling of cell division

Categories Biomedical Applications, Control Applications

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

Turnpike theorems for convex problems with undiscounted integral functionals

Categories Control Applications

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

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

Categories Global Optimization Theory, Quadratic Programming

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

Memory-Aware Parallelized RLT3 for Solving Quadratic Assignment Problems

Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Parallel Algorithms Tags , ,

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

Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

Categories Quadratic Programming Tags , , , ,

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

On the Proximal Jacobian Decomposition of ALM for Multiple-block Separable Convex Minimization Problems and its Relationship to ADMM

Categories Convex Optimization Tags , , , , , ,

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

VERTICES OF SPECTRAHEDRA ARISING FROM THE ELLIPTOPE, THE THETA BODY, AND THEIR RELATIVES

Categories Combinatorial Optimization, Semi-definite Programming Tags , , ,

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

Semidefinite programming and eigenvalue bounds for the graph partition problem

Categories Linear, Cone and Semidefinite Programming Tags , , , ,

The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the total weight of edges joining different sets is optimized. In this paper we simplify a known matrix-lifting semidefinite programming relaxation of the graph partition problem for several classes … Read more

A Hierarchy of Subgraph Projection-Based Semidefinite Relaxations for some NP-Hard Graph Optimization Problems

Categories Branch and Cut Algorithms, Cutting Plane Approaches, Semi-definite Programming

Many important NP-hard combinatorial problems can be efficiently approximated using semidefinite programming relaxations. We propose a new hierarchy of semidefinite relaxations for classes of such problems that based on graphs and for which the projection of the problem onto a subgraph shares the same structure as the original problem. This includes the well-studied max-cut and … Read more