Reformulations and Algorithms for the Optimization of Switching Decisions in Nonlinear Optimal Control

Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

In model-based nonlinear optimal control switching decisions that can be optimized often play an important role. Prominent examples of such hybrid systems are gear switches for transport vehicles or valves in chemical engineering. Optimization algorithms need to take the discrete nature of the variables that model these switching decisions into account. Unnecessarily, for many applications … Read more

Global Optimization for the Design of Space Trajectories

Categories Applications - Science and Engineering, Stochastic Approaches Tags , , , , ,

The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization. We show that many … Read more

Fixed point and Bregman iterative methods for matrix rank minimization

Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The linearly constrained nuclear norm minimization is a convex relaxation of this problem. Although it can be cast as a semidefinite programming problem, the nuclear norm minimization problem is expensive to solve when the … Read more

Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

Categories Stochastic Programming Tags , ,

The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences … Read more

Optimization of Real Asset Portfolio using a Coherent Risk Measure: Application to Oil and Energy Industries

Categories Applications - OR and Management Sciences, Finance and Economics, Stochastic Programming

In many industries, investment is part of the most important planning decisions. In past decades, mathematical programming models have been widely used in capacity planning and facility location to support investment decisions. Such initial techniques evolved to the use of enterprise portfolio management, very common in the energy industry. Increasing concern on risk made of … Read more

Consideration of Gas Supply Contracts with Take-or-pay Clauses in the Brazilian Long-term Energy Planning

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

In Brazil’s long-term energy planning, the dispatch of thermal plants usually varies along a year. Such variation is essentially due to the predominance of the hydraulic mix in the system electric energy supply. For this reason, without preventive measures, a highly irregular cash flow occurs for natural gas (NG) providers, who supply gas for electric … Read more

Incremental-like Bundle Methods with Application to Energy Planning

Categories Nonsmooth Optimization, Production and Logistics, Stochastic Programming Tags , , ,

An important field of application of non-smooth optimization refers to decomposition of large-scale or complex problems by Lagrangian duality. In this setting, the dual problem consists in maximizing a concave non-smooth function that is defined as the sum of sub-functions. The evaluation of each sub-function requires solving a specific optimization sub-problem, with specific computational complexity. … Read more

Convex Relaxations of Non-Convex Mixed Integer Quadratically Constrained Programs: Projected Formulations

Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

A common way to produce a convex relaxation of a Mixed Integer Quadratically Constrained Program (MIQCP) is to lift the problem into a higher dimensional space by introducing variables $Y_{ij}$ to represent each of the products $x_i x_j$ of variables appearing in a quadratic form. One advantage of such extended relaxations is that they can … Read more

Proximal-like contraction methods for monotone variational inequalities in a unified framework

Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Convex Optimization Tags , ,

Approximate proximal point algorithms (abbreviated as APPAs) are classical approaches for convex optimization problems and monotone variational inequalities. To solve the subproblems of these algorithms, the projection method takes the iteration in form of $u^{k+1} = P_{\Omega}[u^k-\alpha_k d^k]$. Interestingly, many of them can be paired such that $%\exists \tilde{u}^k, \tilde{u}^k = P_{\Omega}[u^k – \beta_kF(v^k)] = … Read more

Minimizing the sum of weighted completion times in a concurrent open shop

Categories (Mixed) Integer Linear Programming, Approximation Algorithms, Scheduling Tags , , ,

We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal-dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than … Read more