Exact and Approximate Schemes for Robust Optimization Problems with Decision Dependent Information Discovery

Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed sequentially based on a prescribed filtration. This problem class is useful in a wide range of applications, however, its assimilation is partly limited by … Read more

A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible … Read more

Dual SDDP for risk-averse multistage stochastic programs

Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under time-independence assumptions. We show how to derive a dual formulation for these problems and apply an SDDP algorithm, leading to converging and deterministic upper bounds for risk-averse problems. … Read more

Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning

Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable … Read more

Bishop-Phelps cones given by an equation in Banach spaces

In this work, we study Bishop-Phelps cones (briefly, BP cones) given by an equation in Banach spaces. Due to the special form, these cones enjoy interesting properties. We show that nontrivial BP cones given by an equation form a “large family” in some sense in any Banach space and they can be used to characterize … Read more

A Vectorization Scheme for Nonconvex Set Optimization Problems

In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more

A novel approach for bilevel programs based on Wolfe duality

This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be transformed into a … Read more

A primal heuristic to compute an upper bound set for multi-objective 0-1 linear optimisation problems

This paper presents an algorithm aiming to compute an upper bound set for a multi-objective linear optimisation problem with binary variables (p-01LP). Inspired by the well known « Feasibility Pump » algorithm in single objective optimisation, it belongs to the class of primal heuristics. The proposed algorithm, named « Gravity Machine », aims to deal … Read more

A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix Problem

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of strongly semismooth functions. We show that the so-called local error bound condition does not hold for this system. Thus the … Read more

Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenious norm approach, when the number of points available does not allow to build a complete … Read more