Solving disjunctive optimization problems by generalized semi-infinite optimization techniques

We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods, for our approach neither a conjunctive nor a disjunctive normal form is expected. Applying existing lower level reformulations for the corresponding semi-infinite program we derive conjunctive nonlinear problems without any logical expressions, which can be locally … Read more

Optimality and complexity for constrained optimization problems with nonconvex regularization

In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set and the objective function has a nonsmooth, nonconvex regularizer. Such regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding and non-Lipschitz $L_p$ penalties as special cases. Using the theory of the generalized directional … Read more

Computational Optimization of Gas Compressor Stations: MINLP Models vs. Continuous Reformulations

When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more

Vector Space Decomposition for Linear Programs

This paper describes a vector space decomposition algorithmic framework for linear programming guided by dual feasibility considerations. The resolution process moves from one basic solution to the next according to an exchange mechanism which is defined by a direction and a post-evaluated step size. The core component of this direction is obtained via the smallest … Read more

Separation of Generic Cutting Planes in Branch-and-Price Using a Basis

Dantzig-Wolfe reformulation of a mixed integer program partially convexifies a subset of the constraints, i.e., it implicitly adds all valid inequalities for the associated integer hull. Projecting an optimal basic solution of the reformulation’s LP relaxation to the original space does is in general not yield a basic solution of the original LP relaxation. Cutting … Read more

Perfect dimensional ratios and optimality of some empirical numerical standards

Experience and observations often underlie some widely used numerical characteristics. The problem is in the extent to which such characteristics are optimal. The paper presents results of theoretical analysis of the most frequently used numerical characteristics regarding the number of classes in classification systems, of the base of the number system, and of the level … Read more

Nonsmooth Methods for Control Design with Integral Quadratic Constraints

We develop an optimization technique to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use the fact that IQCs may be transformed into semi-infinite maximum eigenvalue constraints over the frequency axis and approach them via nonsmooth optimization methods. We develop a suitable spectral bundle method and prove its convergence in … Read more

An Overview on Mathematical Programming Approaches for the Deterministic Unit Commitment Problem in Hydro Valleys

With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the plants in hydro valleys is called the hydro unit commitment problem. This problem consists in finding the optimal power production schedule of … Read more

Nonlinear Metric Subregularity

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, … Read more

Multi-period portfolio optimization with alpha decay

The traditional Markowitz MVO approach is based on a single-period model. Single period models do not utilize any data or decisions beyond the rebalancing time horizon with the result that their policies are {\em myopic} in nature. For long-term investors, multi-period optimization offers the opportunity to make {\em wait-and-see} policy decisions by including approximate forecasts … Read more