A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

Categories Applications - OR and Management Sciences

In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope, which has broad applications in power generation scheduling problems. The generalized polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. We derive strong valid inequalities for this polytope by utilizing its specialized structures. … Read more

Inner Approximations of Completely Positive Reformulations of Mixed Binary Quadratic Programs: A Unified Analysis

Categories Global Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, i.e., a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper, we focus on general inner approximations of the cone of completely positive matrices on … Read more

Uniqueness of Market Equilibrium on a Network: A Peak-Load Pricing Approach

Categories Convex Optimization, Finance and Economics, Network Optimization Tags , , ,

In this paper we establish conditions under which uniqueness of market equilibrium is obtained in a setup where prior to trading of electricity, transmission capacities between different market regions are fixed. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested … Read more

On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery

Categories Convex and Nonsmooth Optimization

This paper first proposes another proof of the \textit{necessary and sufficient conditions of solution uniqueness in 1-norm minimization} given recently by H. Zhang, W. Yin, and L. Cheng. The analysis avoids the need of the surjectivity assumption made by these authors and should be mainly appealing by its short length (it can therefore be proposed … Read more

Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization

Categories Convex Optimization Tags , , , ,

The \emph{alternating direction method of multipliers} (ADMM) is a popular and efficient first-order method that has recently found numerous applications, and the proximal ADMM is an important variant of it. The main contributions of this paper are the proposition and the analysis of a class of inertial proximal ADMMs, which unify the basic ideas of … Read more

A general inertial proximal point algorithm for mixed variational inequality problem

Categories Convex Optimization Tags , , ,

In this paper, we first propose a general inertial \emph{proximal point algorithm} (PPA) for the mixed \emph{variational inequality} (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type PPAs. Under certain conditions, we are able to establish the global convergence and nonasymptotic $O(1/k)$ convergence … Read more

The solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction

Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , ,

It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the … Read more

Semi-Infinite Relaxations for the Dynamic Knapsack Problem with Stochastic Item Sizes

Categories 0-1 Programming, Dynamic Programming Tags , ,

We consider a version of the knapsack problem in which an item size is random and revealed only when the decision maker attempts to insert it. After every successful insertion the decision maker can choose the next item dynamically based on the remaining capacity and available items, while an unsuccessful insertion terminates the process. We … Read more

SDDP for multistage stochastic programs: Preprocessing via scenario reduction

Categories Stochastic Programming Tags , , ,

Even with recent enhancements, computation times for large-scale multistage problems with risk-averse objective functions can be very long. Therefore, preprocessing via scenario reduction could be considered as a way to significantly improve the overall performance. Stage-wise backward reduction of single scenarios applied to a fixed branching structure of the tree is a promising tool for … Read more

How to Reach his Desires: Variational Rationality and the Equilibrium Problem on Hadamard Manifolds

Categories Generalized Convexity/Monoticity Tags , , , , ,

In this paper we present a sufficient condition for the existence of a solution for an \mbox{equilibrium} problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we \mbox{propose} a framework for the convergence analysis of a proximal point algorithm to solve this equilibrium \mbox{problem}. Finally, we offer an application to the … Read more