Semidefinite optimization, a spectral approach

This thesis is about mathematical optimization. Mathematical optimization involves the construction of methods to solve optimization problems, which can arise from real-life problems in applied science, when they are mathematically modeled. Examples come from electrical design, engineering, control theory, telecommunication, environment, finance, and logistics. This thesis deals especially with semidefinite optimization problems. Semidefinite programming is … Read more

Symbolic-interval heuristic for bound-constrained minimization

Bound-constrained global optimization helps answer many practical questions in chemistry, molecular biology, economics. Most of algorithms for solution of global optimization problems are a combination of interval methods and exhuastive search. The efficiency of such algorithms is characterized by their ability to detect and eliminate sub-optimal feasible regions. This ability is increased by availability of … Read more

A fast swap-based local search procedure for location problems

We present a new implementation of a widely used swap-based local search procedure for the P-median problem, proposed in 1968 by Teitz and Bart. Our method produces the same output as the best alternatives described in the literature and, even though its worst-case complexity is similar, it can be significantly faster in practice: speedups of … Read more

A hybrid genetic algorithm for the job shop scheduling problem

This paper presents a hybrid genetic algorithm for the Job Shop Scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a … Read more

A D-Induced Duality and Its Applications

This paper attempts to extend the notion of duality for convex cones, by basing it on a pre-described conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the {\em nonnegativity}\/ of the inner-product is replaced by a pre-specified conic ordering, defined by … Read more

Computing Mountain Passes

We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems. We analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at … Read more

Robust regularization

Given a real function on a Euclidean space, we consider its “robust regularization”: the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint … Read more

A GRASP with path-relinking for the p-median problem

Given N customers and a set F of M potential facilities, the P-median problem consists in finding a subset of F with P facilities such that the cost of serving all customers is minimized. This is a well-known NP-complete problem with important applications in location science and classification (clustering). We present here a GRASP (Greedy … Read more

Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization

We prove a sufficient global optimality condition for quadratic optimization with quadratic constraints where the variables are allowed to take -1 and 1 values. We extend the condition to quadratic programs with matrix variables and orthogonality conditions, and in particular, to the quadratic assignment problem. Citation Bilkent University Technical Report, September 2002. Article Download View … Read more

Implementation and Evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0

The SDPA (SemiDefinite Programming Algorithm) is a software package for solving general SDPs(SemiDefinite Programs). It is written in C++ with the help of {\it LAPACK} for numerical linear algebra for dense matrix computation. The purpose of this paper is to present a brief description of the latest version of the SDPA and its high performance … Read more