We revisit the correspondence of competitive partial equilibrium with a social optimum in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources which can be stored. The agents can also trade risk using Arrow-Debreu securities. In this … Read more
The Stochastic Dual Dynamic Programming (SDDP) algorithm has become one of the main tools to address convex multistage stochastic optimal control problem. Recently a large amount of work has been devoted to improve the convergence speed of the algorithm through cut-selection and regularization, or to extend the field of applications to non-linear, integer or risk-averse … Read more
We consider a general class of infinite horizon dynamic programmes where state and control sets are convex and compact subsets of Euclidean spaces and (convex) costs are discounted geometrically. The aim of this work is to provide a convergence result for these problems under as few restrictions as possible. Under certain assumptions on the cost … Read more
For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary … Read more
As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems based on their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by studying IP techniques that can be … Read more
This paper studies risk in a stochastic auction which facilitates the integration of renewable generation in electricity markets. We model market participants who are risk averse and reflect their risk aversion through coherent risk measures. We uncover a closed-form characterization of a risk-averse generator’s optimal pre-commitment behaviour for a given real-time policy, both with and … Read more
This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more
A new branch-and-bound based algorithm for smooth nonconvex multiobjective optimization problems with convex constraints is presented. The algorithm computes an $(\varepsilon,\delta)$-approximation of all globally optimal solutions. We introduce the algorithm which uses selection rules, discarding and termination tests. The discarding tests are the most important aspect, as they examine in different ways whether a box … Read more
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in … Read more
Many problems in real life have more than one decision criterion, referred to as multi-objective optimization (MOO) problems, and the objective functions of these problems are conflicting in most cases. Hence, finding non-dominated solutions is very critical for decision making process. Tri-objective mixed-integer linear programs (TOMILP) are an important subclass of MOOs that are applicable … Read more