Joint dynamic probabilistic constraints with projected linear decision rules

Categories Stochastic Programming

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of … Read more

A multiplier method with a class of penalty functions for convex programming

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

We consider a class of augmented Lagrangian methods for solving convex programming problems with inequality constraints. This class involves a family of penalty functions and specific values of parameters $p,q,\tilde y \in R$ and $c>0$. The penalty family includes the classical modified barrier and the exponential function. The associated proximal method for solving the dual … Read more

General Ellipse Packings in an Optimized Circle Using Embedded Lagrange Multipliers

Categories Applications - Science and Engineering, Global Optimization, Optimization Software and Modeling Systems

The general ellipse packing problem is to find a non-overlapping arrangement of 𝑛 ellipses with (in principle) arbitrary size and orientation parameters inside a given type of container set. Here we consider the general ellipse packing problem with respect to an optimized circle container with minimal radius. Following the review of selected topical literature, we … Read more

The Vehicle Routing Problem with Occasional Drivers

Categories (Mixed) Integer Linear Programming, Meta Heuristics, Transportation Tags , ,

We consider a setting in which a company not only has a fleet of capacitated vehicles and drivers available to make deliveries, but may also use the services of occasional drivers who are willing to make a single delivery using their own vehicle in return for a small compensation if the delivery location is not … Read more

A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen

Categories Combinatorial Optimization, Integer Programming, Transportation Tags , , , , , ,

We address a variant of the vehicle routing problem with time windows (VRPTW) that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to visit this customer. … Read more

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic … Read more

A relaxed-certificate facial reduction algorithm based on subspace intersection

Categories Linear, Cone and Semidefinite Programming, Second-Order Cone Programming Tags , , ,

A “facial reduction”-like regularization algorithm is established for conic optimization problems by relaxing requirements on the reduction certificates. It requires only a linear number of reduction certificates from a constant time-solvable auxiliary problem, but is challenged by representational issues of the exposed reductions. A condition for representability is presented, analyzed for Cartesian product cones, and … Read more

On the computation of convex envelopes for bivariate functions through KKT conditions

Categories Global Optimization Theory Tags , ,

In this paper we exploit a slight variant of a result previously proved in [11] to define a procedure which delivers the convex envelope of some bivariate functions over polytopes. The procedure is based on the solution of a KKT system and simplifies the derivation of the convex envelope with respect to previously proposed techniques. … Read more

Vehicle Routing with Roaming Delivery Locations

Categories Transportation Tags ,

We propose the vehicle routing problem with roaming delivery locations (VRPRDL) to model an innovation in last-mile delivery where a customer’s order is delivered to the trunk of his car. We develop construction and improvement heuristics for the VRPRDL based on two problem-specific techniques: (1) efficiently optimizing the delivery locations for a fixed customer delivery … Read more