COG Reading Group

Monday 16 March 2015

A Weighted Mirror Descent Algorithm for Nonsmooth Convex Optimization

Abstract.

Leader: Ryan Luong
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 9 March 2015

Distributionally Robust Optimization

Abstract. In distributionally robust optimization we seek decisions that perform best in view of the worst-case distribution from within some family of distributions of the uncertain parameters. Distributionally robust models thus relax the unrealistic assumption of a known probability distribution. Instead, they rely on the availability of an ambiguity set, that is, a family of distributions consistent with the decision maker’s prior information. By employing the classical duality theory for moment problems, distributionally robust optimization problems can be reduced to finite dimensional conic programs, which are often computationally tractable.

Leader: Grani Adiwena Hanasusanto
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 2 March 2015

Robust Optimization

Abstract. In this talk we review some of the basic results of robust optimization using the classical duality theory.

Leader: Grani Adiwena Hanasusanto
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 23 February 2015

Convex Optimization: Duality

Abstract. The purpose of the chapter is to provide an in-depth introduction to the Lagrange dual function and problem for convex and non convex optimization problems.

Leader: Sei Howe
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 16 February 2015

Convex Optimization: Duality

Abstract. The purpose of the chapter is to provide an in-depth introduction to the Lagrange dual function and problem for convex and non convex optimization problems.

Leader: Quang Kha Tran
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 9 February 2015

Trust Regions Methods - Global Convergence of the Basic Algorithm.

Abstract. The purpose of the chapter is to provide an in-depth introduction to trust-region methods for the solution of unconstrained problems.

Leader: Juan Campos Salazar
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 2 February 2015

On the complexity of finding first-order critical points in constrained nonlinear optimization.

Abstract. The complexity of finding \epsilon -approximate first-order critical points for the general smooth constrained optimization problem is shown to be noworse that O({\epsilon}^−2) in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply.

Leader: Vahan Hovhannisyan
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 26 January 2015

Concave extensions for nonlinear 0-1 maximization problems

Abstract. A well-known linearization technique for nonlinear 0-1 maximization problems can be viewed as extending any polynomial in 0-1 variables to a concave function defined on [0, 1]". Some properties of this "standard" concave extension are investigated. Polynomials for which the standard extension coincides with the concave envelope are characterized in terms of integrality of a certain polyhedron or balancedness of a certain matrix. The standard extension is proved to be identical to another type of concave extension, defined as the lower envelope of a class of affine functions majorizing the given polynomial.

Leader: Chin Pang Ho (Clint)
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)

Monday 19 January 2015

A symbolic reformulation:spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs

Abstract. This paper presents an algorithm for the solution of nonconvex mixed integer nonlinear programming (MINLP) problems involving general constraints and objective functions. The algorithm employs a symbolic reformulation step that brings the original MINLP problem to an equivalent standard form for which a convex relaxation can be constructed. The reformulated problem is then solved using a spatial branch-and-bound algorithm which branches on both integer and continuous variables. Issues relating to the efficient implementation of this algorithm and its parallelisation are also discussed. The algorithm has been incorporated within the gPROMS process modelling environment and tested on several MINLP problems arising from process engineering applications.

Leader: Georgia Kouyialis
Location: Huxley 217
Time: 5:00 PM (duration: 1 hour)